1 Read data

Read the genotype, phenotype and fitness information of evolved populations of 3000 network topology samples.

jointResultsFolder = "20211201_40node_0.05dens_joint_topos"
pathToJointResultsFolder = paste0("../results/", jointResultsFolder)

# read results and split into sel & neutr
allNetsResults_joint <- read.table(paste0(pathToJointResultsFolder, "/allNetsResults_prepped_joint.txt"), 
                                   sep = "\t", header = TRUE)

# rename nets
allNetsResults_joint[allNetsResults_joint$topo == "BA", "net"] <- 
  allNetsResults_joint[allNetsResults_joint$topo == "BA", "net"] + 1000
allNetsResults_joint[allNetsResults_joint$topo == "WS", "net"] <- 
  allNetsResults_joint[allNetsResults_joint$topo == "WS", "net"] + 2000

allNetsResults_joint$topo <- factor(allNetsResults_joint$topo, levels = c("ER", "BA", "WS"))

# remove genes of degree 1 because they make in and outlink metrics colinear
# reason: when we generate networks we impose that the network must have a single component
# i.e. all genes are connected. Many genes end up having just one connection, which can be either
# an in or outlink. 
allNetsResults_joint <- allNetsResults_joint[allNetsResults_joint$absInStr != 0, ] 
allNetsResults_joint <- allNetsResults_joint[allNetsResults_joint$absOutStr != 0, ] 

selResults <- allNetsResults_joint[allNetsResults_joint$scen == "sel", ]
neutrResults <- allNetsResults_joint[allNetsResults_joint$scen == "neu", ]

# subset responded genes
respondedToSelCutoff <- 0.5

# add which genes responded to selection
selResults$responseToSel <- selResults$s_g_area_abs > respondedToSelCutoff

# subset the genes that responded to selection
respondedGenes <- selResults[selResults$responseToSel == TRUE, ]

1.1 Load packages, functions & colors

library(nlme)
library(MuMIn) # for r.squared in lme models
library(ggplot2)
library(ggpubr) # for the pubclean theme
library(ggridges)
library(gridExtra)
library(cowplot) # for arranging plots
## 
## Attaching package: 'cowplot'
## The following object is masked from 'package:ggpubr':
## 
##     get_legend
library(infotheo)
library(lme4)
## Loading required package: Matrix
## 
## Attaching package: 'lme4'
## The following object is masked from 'package:nlme':
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##     lmList
library(car) # for vif measure
## Loading required package: carData
library(RColorBrewer) # for color palettes
library(latex2exp) # for latex notation in the plots
library(reshape2)
library("Hmisc") # for correlation matrix
## Loading required package: lattice
## Loading required package: survival
## Loading required package: Formula
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## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
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##     format.pval, units
library(corrplot) # for plotting correlation matrix
## corrplot 0.90 loaded
library(ade4) # for PCA
library(factoextra) # for scree plot
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(FSA) # for Dunn tests
## Registered S3 methods overwritten by 'FSA':
##   method       from
##   confint.boot car 
##   hist.boot    car
## ## FSA v0.9.3. See citation('FSA') if used in publication.
## ## Run fishR() for related website and fishR('IFAR') for related book.
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## Attaching package: 'FSA'
## The following object is masked from 'package:car':
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##     bootCase
library(rstatix) # for partial eta for lms
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## Attaching package: 'rstatix'
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##     filter
library(dplyr) # for summarizing dataframes
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## Attaching package: 'dplyr'
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##     src, summarize
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##     intersect, setdiff, setequal, union
# MI 
calcInformation <- function (v1, v2, binNum) {
  
  # discretize 
  d_v1 <- discretize(v1, nbins = binNum);
  d_v2 <- discretize(v2, nbins = binNum)
  
  # mutual information
  I_v1v2 <- mutinformation(d_v1, d_v2);

  return("MI" = I_v1v2)
}

# colors for plots
noiseColor = "#01665e"
genotypeColor = "#7b3294"
phenotypeColor = "#d95f0e"
fitnessColor = "#e78ac3"
neutralityColor = "darkgray"
MIColor = "#2c7fb8"
topoColors = c("ER" = "darkgray", "BA" = "#c51b7d", "WS" = "#4d9221")
netAllResults <- allNetsResults_joint %>%
                  group_by(scen, net) %>%
                  summarize(ave_varP_1 = mean(varP_1),
                            ave_varP_10000 = mean(varP_10000),
                            ave_relDeltaVar_10000 = mean(relDeltaVar_10000),
                            ave_s_g_area_abs = mean(s_g_area_abs),
                            topo = first(topo))
## `summarise()` has grouped output by 'scen'. You can override using the `.groups` argument.
netSelResults <- selResults %>%
                  group_by(scen, net) %>%
                  summarize(ave_varP_1 = mean(varP_1),
                            ave_varP_10000 = mean(varP_10000),
                            ave_relDeltaVar_10000 = mean(relDeltaVar_10000),
                            ave_s_g_area_abs = mean(s_g_area_abs), 
                            ave_responseToSel = length(which(responseToSel)),
                            topo = first(topo))
## `summarise()` has grouped output by 'scen'. You can override using the `.groups` argument.
evolMetricsColnames <- c("meanG_1", "meanG_10000",
                         "meanP_1", "meanP_10000", 
                         "varP_1", "varP_10000", 
                         "CVP_1", "CVP_10000",
                         "noiseP_1", "noiseP_10000", 
                         "FanoP_1", "FanoP_10000",
                         "relDeltaVar_1", "relDeltaVar_10000",
                         "relDeltaCV_1", "relDeltaCV_10000",
                         "relDeltaNoise_1", "relDeltaNoise_10000",
                         "relDeltaFano_1", "relDeltaFano_10000",
                         "s_g_area", "s_g_area_abs", 
                         "s_p_area_relDeltaVar", "s_p_area_relDeltaCV", 
                         "s_p_area_relDeltaNoise", "s_p_area_relDeltaFano")
evolMetricsColnames_ofInterest <- c("varP_1", "relDeltaVar_10000", "s_g_area_abs")
geneSpecificNetMetricsColnames <- c("k_all_inclps", "k_in_inclps", "k_out_inclps", 
                                    "clo_all", "betw", "eigen_centr", 
                                    "str_all_inclps", "str_in_inclps", "str_out_inclps",
                                    "hub_score", "auth_incwght", "auth_excwght",
                                    "absstr_all_inclps", "absInStr", "absOutStr",
                                    "flow", "load", "info", "stress", 
                                    "absInStrT_sqrt", "absOutStrT_sqrt", 
                                    "absInStrT_log1p", "absOutStrT_log1p", 
                                    "absInStrT_log10", "absOutStrT_log10")
geneSpecificNetMetricsColnames_ofInterest <- c("k_all_inclps", "k_in_inclps", "k_out_inclps", 
                                              "clo_all", "betw", "eigen_centr", 
                                              "str_all_inclps", "str_in_inclps", "str_out_inclps",
                                              "hub_score", "auth_incwght", "auth_excwght",
                                              "absstr_all_inclps", "absInStr", "absOutStr",
                                              "flow", "load", "info", "stress")

globalNetMetricsColnames <- c("diam", "meandst", "assort", 
                              "cntr_degr_all", "cntr_indegr", "cntr_outdegr", "cntr_clo_all", "cntr_betw",
                              "ave_k_all_inclps", "ave_k_in_inclps","ave_k_out_inclps")


singletsSelResults <- selResults[!duplicated(selResults$net), c("net", globalNetMetricsColnames)]
netSelResults <- merge(netSelResults, singletsSelResults, by = "net")
singletsAllResults <- allNetsResults_joint[!duplicated(allNetsResults_joint$net), c("net", globalNetMetricsColnames)]
netAllResults <- merge(netAllResults, singletsAllResults, by = "net")

2 Topological effects on distributions of noise metrics

2.1 Preview

# wrap around scenario
ggplot(data = allNetsResults_joint, aes(y = varP_1, x = topo)) +
  geom_boxplot(width = 0.2, alpha = 0.8, outlier.alpha = 0, fill = noiseColor) +
  facet_wrap(~scen) +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  scale_fill_manual(values = c("sel" = noiseColor, "neutr" = noiseColor)) +
    labs(x = "Network topology",
       y = expression(bold("Expr. variance, gen 1"))) 

# wrap around scenario
ggplot(data = allNetsResults_joint, aes(y = varP_10000, x = topo)) +
  geom_boxplot(width = 0.2, alpha = 0.8, outlier.alpha = 0, fill = noiseColor) +
  facet_wrap(~scen) +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  scale_fill_manual(values = c("sel" = noiseColor, "neutr" = noiseColor)) +
  ylab(expression(bold("Expr. variance, gen 10k"))) +
  xlab("Network topology")

# wrap around scenario
ggplot(data = allNetsResults_joint, aes(y = relDeltaVar_10000, x = topo)) +
  geom_boxplot(width = 0.2, alpha = 0.8, outlier.alpha = 0, fill = noiseColor) +
  facet_wrap(~scen) +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  scale_fill_manual(values = c("sel" = noiseColor, "neutr" = noiseColor)) +
  ylab(expression(bold("Rel."~Delta~"expr. variance"))) +
  xlab("Network topology")
## Warning: Removed 130 rows containing non-finite values (stat_boxplot).

# wrap around scenario
ggplot(data = allNetsResults_joint, aes(y = s_g_area_abs, x = topo)) +
  geom_boxplot(width = 0.2, alpha = 0.8, outlier.alpha = 0, fill = genotypeColor) +
  facet_wrap(~scen) +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  scale_fill_manual(values = c("sel" = genotypeColor, "neutr" = genotypeColor)) +
  ylab(expression(paste(bold("Selective pressure "), "|", bold(p), "|"))) +
  xlab("Network topology")

my_comparisons <- list( c("ER", "BA"), c("BA", "WS"), c("WS", "ER") )

# just selection
plot_varFirstgen_sel <- ggplot(selResults, aes(y = varP_1, x = topo)) +
  geom_violin(aes(fill = topo), trim = TRUE) +
  geom_boxplot(width = 0.05, alpha = 1, outlier.alpha = 0, fill = "white") +
               stat_compare_means(comparisons = my_comparisons, label = "p.signif", method = "wilcox.test") +
  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
               hjust = 1.25, vjust = -2, color = "black", aes(label=round(..y.., digits=2))) +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "right") +
  scale_fill_manual(values = topoColors) +
  labs(x = "Network topology",
       y = "Expr. variance, gen 1",
       fill = "Topology")
plot_varFirstgen_sel

ggsave(filename = sprintf("plot_varFirstgen_sel.png"),
       plot = plot_varFirstgen_sel, 
       path = pathToPlotsFolder,
       device = "png", scale = 2, width = 6, height = 5.5, units = "cm",
       dpi = 300, limitsize = TRUE)

# just selection
plot_varLastgen_sel <- ggplot(selResults, aes(y = varP_10000, x = topo)) +
  geom_violin(aes(fill = topo), trim = TRUE) +
  geom_boxplot(width = 0.05, alpha = 1, outlier.alpha = 0, fill = "white") +
               stat_compare_means(comparisons = my_comparisons, label = "p.signif", method = "wilcox.test") +
  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
               hjust = 1.25, vjust = -2, color = "black", aes(label=round(..y.., digits=2))) +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "right") +
  scale_fill_manual(values = topoColors) +
  labs(x = "Network topology",
       y = "Expr. variance, gen 10k",
       fill = "Topology")
plot_varLastgen_sel

ggsave(filename = sprintf("plot_varLastgen_sel.png"),
       plot = plot_varLastgen_sel, 
       path = pathToPlotsFolder,
       device = "png", scale = 2, width = 6, height = 5.5, units = "cm",
       dpi = 300, limitsize = TRUE)

# just selection
plot_relDeltaVar_sel <- ggplot(selResults, aes(y = relDeltaVar_10000, x = topo)) +
  geom_violin(aes(fill = topo), trim = TRUE) +
  geom_boxplot(width = 0.1, alpha = 1, outlier.alpha = 0, fill = "white") +
  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
               hjust = 1.25, vjust = -2, color = "black", aes(label = round(..y.., digits = 3))) +
  stat_compare_means(comparisons = my_comparisons, label = "p.signif", method = "wilcox.test") +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "right") +
  scale_fill_manual(values = topoColors) +
  labs(x = "Network topology",
       y = expression(bold("Rel."~Delta~"expr. variance")),
       fill = "Topology")
plot_relDeltaVar_sel
## Warning: Removed 90 rows containing non-finite values (stat_ydensity).
## Warning: Removed 90 rows containing non-finite values (stat_boxplot).
## Warning: Removed 90 rows containing non-finite values (stat_summary).
## Warning: Removed 90 rows containing non-finite values (stat_signif).

ggsave(filename = sprintf("plot_relDeltaVar_sel.png"),
       plot = plot_relDeltaVar_sel, 
       path = pathToPlotsFolder,
       device = "png", scale = 2, width = 6, height = 5.5, units = "cm",
       dpi = 300, limitsize = TRUE)
## Warning: Removed 90 rows containing non-finite values (stat_ydensity).
## Warning: Removed 90 rows containing non-finite values (stat_boxplot).
## Warning: Removed 90 rows containing non-finite values (stat_summary).
## Warning: Removed 90 rows containing non-finite values (stat_signif).
# just selection
plot_selpress_sel <- ggplot(selResults, aes(y = s_g_area_abs, x = topo)) +
  geom_violin(aes(fill = topo), trim = TRUE) +
  geom_boxplot(width = 0.1, alpha = 1, outlier.alpha = 0, fill = "white") +
  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
               hjust = 1.25, vjust = 3, color = "black", aes(label = round(..y.., digits = 3))) +
  stat_compare_means(comparisons = my_comparisons, label = "p.signif", method = "wilcox.test") +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "right") +
  scale_fill_manual(values = topoColors) +
  labs(x = "Network topology",
       y = expression(paste(bold("Selective pressure "), "|", bold(p), "|")),
       fill = "Topology")
plot_selpress_sel

ggsave(filename = sprintf("plot_selpress_sel.png"),
       plot = plot_selpress_sel,
       path = pathToPlotsFolder,
       device = "png", scale = 2, width = 6, height = 5.5, units = "cm",
       dpi = 300, limitsize = TRUE)

plot_violin_metrics_per_topo <- plot_grid(plot_varFirstgen_sel,
                        plot_varLastgen_sel,
                        plot_relDeltaVar_sel,
                        plot_selpress_sel,
                        scale = c(0.95, 0.95, 0.95, 0.95),
                        labels = "AUTO",
                        label_size = 20,
                        label_fontface = "bold")
## Warning: Removed 90 rows containing non-finite values (stat_ydensity).
## Warning: Removed 90 rows containing non-finite values (stat_boxplot).
## Warning: Removed 90 rows containing non-finite values (stat_summary).
## Warning: Removed 90 rows containing non-finite values (stat_signif).
ggsave(filename = sprintf("plot_violin_metrics_per_topo.png"),
       plot = plot_violin_metrics_per_topo, 
       bg = "white",
       path = pathToPlotsFolder,
       device = "png", scale = 1.8, width = 17, height = 12, units = "cm",
       dpi = 300, limitsize = TRUE)
ggsave(filename = sprintf("plot_violin_metrics_per_topo.tiff"),
       plot = plot_violin_metrics_per_topo, 
       bg = "white",
       path = pathToPlotsFolder,
       device = "tiff", scale = 1.8, width = 17, height = 12, units = "cm",
       dpi = 300, limitsize = TRUE)

2.2 Comparisons

summary(selResults$varP_1[selResults$topo == "BA"])
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
##    0.1648  139.0104  282.1687  338.6733  458.7734 2166.1780
summary(selResults$varP_1[selResults$topo == "ER"])
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
##    0.0001  131.4944  231.0748  353.3577  429.9174 2397.0850
summary(selResults$varP_1[selResults$topo == "WS"])
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
##    0.0001  130.1976  240.8380  395.2082  509.2964 2326.2150
summary(selResults$varP_10000[selResults$topo == "BA"])
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   3.953   8.371   9.901  12.792 459.084
summary(selResults$varP_10000[selResults$topo == "ER"])
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
##    0.000    4.644    8.832   22.482   16.325 2425.164
summary(selResults$varP_10000[selResults$topo == "WS"])
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
##    0.000    3.777    8.387   24.483   18.735 2130.139
summary(selResults$relDeltaVar_10000[selResults$topo == "BA"])
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's 
## -1.00000 -0.96262 -0.94869 -0.94439 -0.93212  0.01953        4
summary(selResults$relDeltaVar_10000[selResults$topo == "ER"])
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
## -1.0000 -0.9508 -0.9288 -0.9123 -0.9004  1.0000      33
summary(selResults$relDeltaVar_10000[selResults$topo == "WS"])
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
## -1.0000 -0.9576 -0.9347 -0.9163 -0.9046  0.5278      53
summary(selResults$s_g_area_abs[selResults$topo == "BA"])
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## 0.0000025 0.8600859 0.8966813 0.8057883 0.9308498 0.9855338
summary(selResults$s_g_area_abs[selResults$topo == "ER"])
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.00001 0.82738 0.88613 0.77038 0.92574 0.98224
summary(selResults$s_g_area_abs[selResults$topo == "WS"])
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## 0.0000021 0.7913765 0.8913866 0.7449805 0.9337625 0.9836893
kruskal.test(varP_1 ~ topo, data = selResults)
## 
##  Kruskal-Wallis rank sum test
## 
## data:  varP_1 by topo
## Kruskal-Wallis chi-squared = 69.922, df = 2, p-value = 6.555e-16
kruskal.test(varP_10000 ~ topo, data = selResults)
## 
##  Kruskal-Wallis rank sum test
## 
## data:  varP_10000 by topo
## Kruskal-Wallis chi-squared = 255.8, df = 2, p-value < 2.2e-16
kruskal.test(relDeltaVar_10000 ~ topo, data = selResults)
## 
##  Kruskal-Wallis rank sum test
## 
## data:  relDeltaVar_10000 by topo
## Kruskal-Wallis chi-squared = 2830.3, df = 2, p-value < 2.2e-16
kruskal.test(s_g_area_abs ~ topo, data = selResults)
## 
##  Kruskal-Wallis rank sum test
## 
## data:  s_g_area_abs by topo
## Kruskal-Wallis chi-squared = 296.08, df = 2, p-value < 2.2e-16
pairwise.wilcox.test(selResults$varP_1, selResults$topo, paired = FALSE, p.adjust.method = "BH")
## 
##  Pairwise comparisons using Wilcoxon rank sum test 
## 
## data:  selResults$varP_1 and selResults$topo 
## 
##    ER      BA  
## BA 1.8e-14 -   
## WS 6.8e-11 0.11
## 
## P value adjustment method: BH
pairwise.wilcox.test(selResults$varP_10000, selResults$topo, paired = FALSE, p.adjust.method = "BH")
## 
##  Pairwise comparisons using Wilcoxon rank sum test 
## 
## data:  selResults$varP_10000 and selResults$topo 
## 
##    ER      BA     
## BA < 2e-16 -      
## WS 6.1e-05 < 2e-16
## 
## P value adjustment method: BH
pairwise.wilcox.test(selResults$relDeltaVar_10000, selResults$topo, paired = FALSE, p.adjust.method = "BH")
## 
##  Pairwise comparisons using Wilcoxon rank sum test 
## 
## data:  selResults$relDeltaVar_10000 and selResults$topo 
## 
##    ER     BA    
## BA <2e-16 -     
## WS <2e-16 <2e-16
## 
## P value adjustment method: BH
pairwise.wilcox.test(selResults$s_g_area_abs, selResults$topo, paired = FALSE, p.adjust.method = "BH")
## 
##  Pairwise comparisons using Wilcoxon rank sum test 
## 
## data:  selResults$s_g_area_abs and selResults$topo 
## 
##    ER      BA     
## BA < 2e-16 -      
## WS 9.4e-07 < 2e-16
## 
## P value adjustment method: BH
# ER to BA
wilcox.test(selResults$varP_1[selResults$topo == "ER"], selResults$varP_1[selResults$topo == "BA"],
            alternative = "less")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$varP_1[selResults$topo == "ER"] and selResults$varP_1[selResults$topo == "BA"]
## W = 146955679, p-value = 3.081e-15
## alternative hypothesis: true location shift is less than 0
wilcox.test(selResults$varP_1[selResults$topo == "ER"], selResults$varP_1[selResults$topo == "BA"],
            alternative = "greater")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$varP_1[selResults$topo == "ER"] and selResults$varP_1[selResults$topo == "BA"]
## W = 146955679, p-value = 1
## alternative hypothesis: true location shift is greater than 0
# BA to WS
wilcox.test(selResults$varP_1[selResults$topo == "BA"], selResults$varP_1[selResults$topo == "WS"],
            alternative = "less")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$varP_1[selResults$topo == "BA"] and selResults$varP_1[selResults$topo == "WS"]
## W = 196526721, p-value = 0.9456
## alternative hypothesis: true location shift is less than 0
wilcox.test(selResults$varP_1[selResults$topo == "BA"], selResults$varP_1[selResults$topo == "WS"],
            alternative = "greater")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$varP_1[selResults$topo == "BA"] and selResults$varP_1[selResults$topo == "WS"]
## W = 196526721, p-value = 0.05441
## alternative hypothesis: true location shift is greater than 0
# WS to ER
wilcox.test(selResults$varP_1[selResults$topo == "WS"], selResults$varP_1[selResults$topo == "ER"],
            alternative = "less")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$varP_1[selResults$topo == "WS"] and selResults$varP_1[selResults$topo == "ER"]
## W = 457296947, p-value = 1
## alternative hypothesis: true location shift is less than 0
wilcox.test(selResults$varP_1[selResults$topo == "WS"], selResults$varP_1[selResults$topo == "ER"],
            alternative = "greater")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$varP_1[selResults$topo == "WS"] and selResults$varP_1[selResults$topo == "ER"]
## W = 457296947, p-value = 2.271e-11
## alternative hypothesis: true location shift is greater than 0
# ER to BA
wilcox.test(selResults$varP_10000[selResults$topo == "ER"], selResults$varP_10000[selResults$topo == "BA"],
            alternative = "less")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$varP_10000[selResults$topo == "ER"] and selResults$varP_10000[selResults$topo == "BA"]
## W = 170461586, p-value = 1
## alternative hypothesis: true location shift is less than 0
wilcox.test(selResults$varP_10000[selResults$topo == "ER"], selResults$varP_10000[selResults$topo == "BA"],
            alternative = "greater")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$varP_10000[selResults$topo == "ER"] and selResults$varP_10000[selResults$topo == "BA"]
## W = 170461586, p-value < 2.2e-16
## alternative hypothesis: true location shift is greater than 0
# BA to WS
wilcox.test(selResults$varP_10000[selResults$topo == "BA"], selResults$varP_10000[selResults$topo == "WS"],
            alternative = "less")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$varP_10000[selResults$topo == "BA"] and selResults$varP_10000[selResults$topo == "WS"]
## W = 178769580, p-value < 2.2e-16
## alternative hypothesis: true location shift is less than 0
wilcox.test(selResults$varP_10000[selResults$topo == "BA"], selResults$varP_10000[selResults$topo == "WS"],
            alternative = "greater")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$varP_10000[selResults$topo == "BA"] and selResults$varP_10000[selResults$topo == "WS"]
## W = 178769580, p-value = 1
## alternative hypothesis: true location shift is greater than 0
# WS to ER
wilcox.test(selResults$varP_10000[selResults$topo == "WS"], selResults$varP_10000[selResults$topo == "ER"],
            alternative = "less")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$varP_10000[selResults$topo == "WS"] and selResults$varP_10000[selResults$topo == "ER"]
## W = 434993181, p-value = 3.03e-05
## alternative hypothesis: true location shift is less than 0
wilcox.test(selResults$varP_10000[selResults$topo == "WS"], selResults$varP_10000[selResults$topo == "ER"],
            alternative = "greater")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$varP_10000[selResults$topo == "WS"] and selResults$varP_10000[selResults$topo == "ER"]
## W = 434993181, p-value = 1
## alternative hypothesis: true location shift is greater than 0
# ER to BA
wilcox.test(selResults$relDeltaVar_10000[selResults$topo == "ER"], selResults$relDeltaVar_10000[selResults$topo == "BA"],
            alternative = "less")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$relDeltaVar_10000[selResults$topo == "ER"] and selResults$relDeltaVar_10000[selResults$topo == "BA"]
## W = 208663610, p-value = 1
## alternative hypothesis: true location shift is less than 0
wilcox.test(selResults$relDeltaVar_10000[selResults$topo == "ER"], selResults$relDeltaVar_10000[selResults$topo == "BA"],
            alternative = "greater")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$relDeltaVar_10000[selResults$topo == "ER"] and selResults$relDeltaVar_10000[selResults$topo == "BA"]
## W = 208663610, p-value < 2.2e-16
## alternative hypothesis: true location shift is greater than 0
# BA to WS
wilcox.test(selResults$relDeltaVar_10000[selResults$topo == "BA"], selResults$relDeltaVar_10000[selResults$topo == "WS"],
            alternative = "less")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$relDeltaVar_10000[selResults$topo == "BA"] and selResults$relDeltaVar_10000[selResults$topo == "WS"]
## W = 145879932, p-value < 2.2e-16
## alternative hypothesis: true location shift is less than 0
wilcox.test(selResults$relDeltaVar_10000[selResults$topo == "BA"], selResults$relDeltaVar_10000[selResults$topo == "WS"],
            alternative = "greater")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$relDeltaVar_10000[selResults$topo == "BA"] and selResults$relDeltaVar_10000[selResults$topo == "WS"]
## W = 145879932, p-value = 1
## alternative hypothesis: true location shift is greater than 0
# WS to ER
wilcox.test(selResults$relDeltaVar_10000[selResults$topo == "WS"], selResults$relDeltaVar_10000[selResults$topo == "ER"],
            alternative = "less")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$relDeltaVar_10000[selResults$topo == "WS"] and selResults$relDeltaVar_10000[selResults$topo == "ER"]
## W = 407500592, p-value < 2.2e-16
## alternative hypothesis: true location shift is less than 0
wilcox.test(selResults$relDeltaVar_10000[selResults$topo == "WS"], selResults$relDeltaVar_10000[selResults$topo == "ER"],
            alternative = "greater")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$relDeltaVar_10000[selResults$topo == "WS"] and selResults$relDeltaVar_10000[selResults$topo == "ER"]
## W = 407500592, p-value = 1
## alternative hypothesis: true location shift is greater than 0
# ER to BA
wilcox.test(selResults$s_g_area_abs[selResults$topo == "ER"], selResults$s_g_area_abs[selResults$topo == "BA"],
            alternative = "less")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$s_g_area_abs[selResults$topo == "ER"] and selResults$s_g_area_abs[selResults$topo == "BA"]
## W = 137097094, p-value < 2.2e-16
## alternative hypothesis: true location shift is less than 0
wilcox.test(selResults$s_g_area_abs[selResults$topo == "ER"], selResults$s_g_area_abs[selResults$topo == "BA"],
            alternative = "greater")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$s_g_area_abs[selResults$topo == "ER"] and selResults$s_g_area_abs[selResults$topo == "BA"]
## W = 137097094, p-value = 1
## alternative hypothesis: true location shift is greater than 0
# BA to WS
wilcox.test(selResults$s_g_area_abs[selResults$topo == "BA"], selResults$s_g_area_abs[selResults$topo == "WS"],
            alternative = "less")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$s_g_area_abs[selResults$topo == "BA"] and selResults$s_g_area_abs[selResults$topo == "WS"]
## W = 210471566, p-value = 1
## alternative hypothesis: true location shift is less than 0
wilcox.test(selResults$s_g_area_abs[selResults$topo == "BA"], selResults$s_g_area_abs[selResults$topo == "WS"],
            alternative = "greater")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$s_g_area_abs[selResults$topo == "BA"] and selResults$s_g_area_abs[selResults$topo == "WS"]
## W = 210471566, p-value < 2.2e-16
## alternative hypothesis: true location shift is greater than 0
# WS to ER
wilcox.test(selResults$s_g_area_abs[selResults$topo == "WS"], selResults$s_g_area_abs[selResults$topo == "ER"],
            alternative = "less")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$s_g_area_abs[selResults$topo == "WS"] and selResults$s_g_area_abs[selResults$topo == "ER"]
## W = 453756137, p-value = 1
## alternative hypothesis: true location shift is less than 0
wilcox.test(selResults$s_g_area_abs[selResults$topo == "WS"], selResults$s_g_area_abs[selResults$topo == "ER"],
            alternative = "greater")
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  selResults$s_g_area_abs[selResults$topo == "WS"] and selResults$s_g_area_abs[selResults$topo == "ER"]
## W = 453756137, p-value = 4.716e-07
## alternative hypothesis: true location shift is greater than 0
dunnTest(varP_1 ~ topo, data = selResults, method = "bh")
## Dunn (1964) Kruskal-Wallis multiple comparison
##   p-values adjusted with the Benjamini-Hochberg method.
##   Comparison         Z      P.unadj        P.adj
## 1    BA - ER  7.158985 8.127635e-13 2.438290e-12
## 2    BA - WS  2.130387 3.313972e-02 3.313972e-02
## 3    ER - WS -6.887795 5.666368e-12 8.499552e-12
dunnTest(varP_10000 ~ topo, data = selResults, method = "bh")
## Dunn (1964) Kruskal-Wallis multiple comparison
##   p-values adjusted with the Benjamini-Hochberg method.
##   Comparison         Z      P.unadj        P.adj
## 1    BA - ER -15.76887 5.095664e-56 1.528699e-55
## 2    BA - WS -13.18042 1.137614e-39 1.706421e-39
## 3    ER - WS   4.06425 4.818725e-05 4.818725e-05
dunnTest(relDeltaVar_10000 ~ topo, data = selResults, method = "bh")
## Warning: Some rows deleted from 'x' and 'g' because missing data.
## Dunn (1964) Kruskal-Wallis multiple comparison
##   p-values adjusted with the Benjamini-Hochberg method.
##   Comparison         Z      P.unadj        P.adj
## 1    BA - ER -52.96934 0.000000e+00 0.000000e+00
## 2    BA - WS -41.46320 0.000000e+00 0.000000e+00
## 3    ER - WS  17.32305 3.152052e-67 3.152052e-67
dunnTest(s_g_area_abs ~ topo, data = selResults, method = "bh")
## Dunn (1964) Kruskal-Wallis multiple comparison
##   p-values adjusted with the Benjamini-Hochberg method.
##   Comparison         Z      P.unadj        P.adj
## 1    BA - ER 17.088478 1.808336e-65 5.425007e-65
## 2    BA - WS 13.669766 1.538893e-42 2.308339e-42
## 3    ER - WS -5.207388 1.915178e-07 1.915178e-07
lmeModel <- lm(ave_varP_1 ~ topo, 
               data = netSelResults)
summary(lmeModel)
## 
## Call:
## lm(formula = ave_varP_1 ~ topo, data = netSelResults)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -262.26  -78.16  -15.13   63.70  606.50 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  352.694      3.499 100.807  < 2e-16 ***
## topoBA       -18.333      4.948  -3.705 0.000215 ***
## topoWS        40.416      4.948   8.168 4.56e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 110.6 on 2997 degrees of freedom
## Multiple R-squared:  0.04694,    Adjusted R-squared:  0.04631 
## F-statistic: 73.81 on 2 and 2997 DF,  p-value: < 2.2e-16
r.squaredGLMM(lmeModel)
## Warning: 'r.squaredGLMM' now calculates a revised statistic. See the help page.
##             R2m        R2c
## [1,] 0.04691374 0.04691374
lmeModel <- lm(ave_varP_10000 ~ topo, 
               data = netSelResults)
summary(lmeModel)
## 
## Call:
## lm(formula = ave_varP_10000 ~ topo, data = netSelResults)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -17.85 -10.07  -3.59   0.21 861.43 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   22.106      1.094  20.210  < 2e-16 ***
## topoBA       -12.401      1.547  -8.017 1.54e-15 ***
## topoWS         2.027      1.547   1.310     0.19    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 34.59 on 2997 degrees of freedom
## Multiple R-squared:  0.03291,    Adjusted R-squared:  0.03227 
## F-statistic:    51 on 2 and 2997 DF,  p-value: < 2.2e-16
r.squaredGLMM(lmeModel)
##             R2m        R2c
## [1,] 0.03288984 0.03288984
lmeModel <- lm(ave_relDeltaVar_10000 ~ topo, 
              data = netSelResults[!is.na(netSelResults$ave_relDeltaVar_10000), ])

summary(lmeModel)
## 
## Call:
## lm(formula = ave_relDeltaVar_10000 ~ topo, data = netSelResults[!is.na(netSelResults$ave_relDeltaVar_10000), 
##     ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.03860 -0.01424 -0.00628  0.00266  0.63702 
## 
## Coefficients:
##              Estimate Std. Error  t value Pr(>|t|)    
## (Intercept) -0.912812   0.001304 -700.007   <2e-16 ***
## topoBA      -0.032025   0.001832  -17.485   <2e-16 ***
## topoWS      -0.004418   0.001854   -2.382   0.0173 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04059 on 2910 degrees of freedom
## Multiple R-squared:  0.1101, Adjusted R-squared:  0.1095 
## F-statistic: 179.9 on 2 and 2910 DF,  p-value: < 2.2e-16
r.squaredGLMM(lmeModel)
##            R2m       R2c
## [1,] 0.1099949 0.1099949
lmeModel <- lm(ave_s_g_area_abs ~ topo,
               data = netSelResults)

summary(lmeModel)
## 
## Call:
## lm(formula = ave_s_g_area_abs ~ topo, data = netSelResults)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.67253 -0.03775  0.01170  0.04729  0.13888 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.770923   0.002406 320.368  < 2e-16 ***
## topoBA       0.033993   0.003403   9.989  < 2e-16 ***
## topoWS      -0.025315   0.003403  -7.439 1.32e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0761 on 2997 degrees of freedom
## Multiple R-squared:  0.09261,    Adjusted R-squared:  0.09201 
## F-statistic: 152.9 on 2 and 2997 DF,  p-value: < 2.2e-16
r.squaredGLMM(lmeModel)
##             R2m        R2c
## [1,] 0.09255582 0.09255582

3 Topological effects on local network metrics

3.1 Logistic regression

logRegModel <- glmer(responseToSel ~ (absInStrT_sqrt + absOutStrT_sqrt)*topo + (1|net), 
                   data = selResults,
                   family = binomial,
                   control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5)))
summary(logRegModel)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: responseToSel ~ (absInStrT_sqrt + absOutStrT_sqrt) * topo + (1 |  
##     net)
##    Data: selResults
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+05))
## 
##      AIC      BIC   logLik deviance df.resid 
##  50728.0  50819.8 -25354.0  50708.0    71595 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -9.5125  0.1713  0.2554  0.3982  3.7128 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  net    (Intercept) 0.1398   0.3739  
## Number of obs: 71605, groups:  net, 3000
## 
## Fixed effects:
##                         Estimate Std. Error z value Pr(>|z|)    
## (Intercept)             5.086008   0.077100  65.967  < 2e-16 ***
## absInStrT_sqrt         -1.802274   0.031955 -56.400  < 2e-16 ***
## absOutStrT_sqrt        -0.236429   0.029744  -7.949 1.88e-15 ***
## topoBA                  1.690235   0.174331   9.696  < 2e-16 ***
## topoWS                 -0.265964   0.104774  -2.538 0.011135 *  
## absInStrT_sqrt:topoBA  -0.314604   0.081584  -3.856 0.000115 ***
## absInStrT_sqrt:topoWS  -0.066180   0.043605  -1.518 0.129082    
## absOutStrT_sqrt:topoBA -0.259738   0.033749  -7.696 1.40e-14 ***
## absOutStrT_sqrt:topoWS  0.009153   0.040944   0.224 0.823116    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) abIST_ abOST_ topoBA topoWS aIST_:B aIST_:W aOST_:B
## absInStrT_s -0.775                                                    
## absOtStrT_s -0.591  0.048                                             
## topoBA      -0.432  0.334  0.262                                      
## topoWS      -0.726  0.563  0.435  0.320                               
## absInST_:BA  0.297 -0.386 -0.019 -0.911 -0.219                        
## absInST_:WS  0.559 -0.725 -0.035 -0.247 -0.776  0.284                 
## absOtST_:BA  0.517 -0.038 -0.881 -0.468 -0.383  0.164   0.030         
## absOtST_:WS  0.430 -0.035 -0.726 -0.190 -0.624  0.013   0.086   0.640

3.2 Local network metrics

lmeModel <- lme(varP_1 ~ (absInStrT_sqrt + absOutStrT_sqrt)*topo, 
                data = selResults,
                weights = varExp(form = ~absInStrT_sqrt),
                random = ~1|net,
                method = "ML") 
summary(lmeModel)
## Linear mixed-effects model fit by maximum likelihood
##  Data: selResults 
##        AIC      BIC    logLik
##   988557.4 988667.6 -494266.7
## 
## Random effects:
##  Formula: ~1 | net
##         (Intercept) Residual
## StdDev:    41.17568 55.01751
## 
## Variance function:
##  Structure: Exponential of variance covariate
##  Formula: ~absInStrT_sqrt 
##  Parameter estimates:
##    expon 
## 1.036034 
## Fixed effects: varP_1 ~ (absInStrT_sqrt + absOutStrT_sqrt) * topo 
##                            Value Std.Error    DF   t-value p-value
## (Intercept)             48.15409  3.826547 68599  12.58422  0.0000
## absInStrT_sqrt         230.94334  2.646290 68599  87.27061  0.0000
## absOutStrT_sqrt        -21.63507  1.644374 68599 -13.15703  0.0000
## topoBA                  26.91664  8.073025  2997   3.33415  0.0009
## topoWS                 -33.41109  5.581999  2997  -5.98551  0.0000
## absInStrT_sqrt:topoBA  -37.01439  5.502201 68599  -6.72720  0.0000
## absInStrT_sqrt:topoWS   51.96763  3.595365 68599  14.45406  0.0000
## absOutStrT_sqrt:topoBA  -3.16029  1.971353 68599  -1.60311  0.1089
## absOutStrT_sqrt:topoWS   3.18058  2.415215 68599   1.31689  0.1879
##  Correlation: 
##                        (Intr) abIST_ abOST_ topoBA topoWS aIST_:B aIST_:W
## absInStrT_sqrt         -0.658                                            
## absOutStrT_sqrt        -0.683  0.110                                     
## topoBA                 -0.474  0.312  0.324                              
## topoWS                 -0.686  0.451  0.468  0.325                       
## absInStrT_sqrt:topoBA   0.316 -0.481 -0.053 -0.829 -0.217                
## absInStrT_sqrt:topoWS   0.484 -0.736 -0.081 -0.230 -0.650  0.354         
## absOutStrT_sqrt:topoBA  0.570 -0.091 -0.834 -0.582 -0.391  0.224   0.067 
## absOutStrT_sqrt:topoWS  0.465 -0.075 -0.681 -0.220 -0.715  0.036   0.130 
##                        aOST_:B
## absInStrT_sqrt                
## absOutStrT_sqrt               
## topoBA                        
## topoWS                        
## absInStrT_sqrt:topoBA         
## absInStrT_sqrt:topoWS         
## absOutStrT_sqrt:topoBA        
## absOutStrT_sqrt:topoWS  0.568 
## 
## Standardized Within-Group Residuals:
##        Min         Q1        Med         Q3        Max 
## -3.0554341 -0.6144405 -0.1431631  0.4085847  7.7066634 
## 
## Number of Observations: 71605
## Number of Groups: 3000
r.squaredGLMM(lmeModel)
##            R2m       R2c
## [1,] 0.8292969 0.8905832
lmeModel <- lme(relDeltaVar_10000 ~ (absInStrT_sqrt + absOutStrT_sqrt)*topo, 
                data = respondedGenes,
                weights = varExp(form = ~absInStrT_sqrt),
                random = ~1|net,
                method = "ML") 
summary(lmeModel)
## Linear mixed-effects model fit by maximum likelihood
##  Data: respondedGenes 
##         AIC       BIC  logLik
##   -178667.6 -178559.5 89345.8
## 
## Random effects:
##  Formula: ~1 | net
##         (Intercept)   Residual
## StdDev:  0.02577517 0.03457918
## 
## Variance function:
##  Structure: Exponential of variance covariate
##  Formula: ~absInStrT_sqrt 
##  Parameter estimates:
##     expon 
## 0.3238401 
## Fixed effects: relDeltaVar_10000 ~ (absInStrT_sqrt + absOutStrT_sqrt) * topo 
##                             Value    Std.Error    DF   t-value p-value
## (Intercept)            -0.8920085 0.0014150225 57540 -630.3846  0.0000
## absInStrT_sqrt          0.0041702 0.0006828856 57540    6.1068  0.0000
## absOutStrT_sqrt        -0.0175873 0.0005458196 57540  -32.2219  0.0000
## topoBA                 -0.0130093 0.0026880429  2997   -4.8397  0.0000
## topoWS                 -0.0100136 0.0020553971  2997   -4.8719  0.0000
## absInStrT_sqrt:topoBA  -0.0173448 0.0014474836 57540  -11.9828  0.0000
## absInStrT_sqrt:topoWS   0.0047507 0.0009483660 57540    5.0094  0.0000
## absOutStrT_sqrt:topoBA  0.0078031 0.0006505324 57540   11.9949  0.0000
## absOutStrT_sqrt:topoWS -0.0007539 0.0007937504 57540   -0.9498  0.3422
##  Correlation: 
##                        (Intr) abIST_ abOST_ topoBA topoWS aIST_:B aIST_:W
## absInStrT_sqrt         -0.565                                            
## absOutStrT_sqrt        -0.579  0.071                                     
## topoBA                 -0.526  0.297  0.305                              
## topoWS                 -0.688  0.389  0.399  0.362                       
## absInStrT_sqrt:topoBA   0.267 -0.472 -0.034 -0.785 -0.183                
## absInStrT_sqrt:topoWS   0.407 -0.720 -0.051 -0.214 -0.574  0.340         
## absOutStrT_sqrt:topoBA  0.486 -0.060 -0.839 -0.514 -0.334  0.196   0.043 
## absOutStrT_sqrt:topoWS  0.398 -0.049 -0.688 -0.210 -0.613  0.023   0.111 
##                        aOST_:B
## absInStrT_sqrt                
## absOutStrT_sqrt               
## topoBA                        
## topoWS                        
## absInStrT_sqrt:topoBA         
## absInStrT_sqrt:topoWS         
## absOutStrT_sqrt:topoBA        
## absOutStrT_sqrt:topoWS  0.577 
## 
## Standardized Within-Group Residuals:
##        Min         Q1        Med         Q3        Max 
## -7.1611542 -0.4561679 -0.1423956  0.2539409 24.3732650 
## 
## Number of Observations: 60546
## Number of Groups: 3000
r.squaredGLMM(lmeModel)
##            R2m       R2c
## [1,] 0.1224098 0.4358563
lmeModel <- lme(s_g_area_abs ~ (absInStrT_sqrt + absOutStrT_sqrt)*topo, 
                data = respondedGenes,
                weights = varExp(form = ~absInStrT_sqrt),
                random = ~1|net,
                method = "ML") 
summary(lmeModel)
## Linear mixed-effects model fit by maximum likelihood
##  Data: respondedGenes 
##         AIC       BIC   logLik
##   -168395.4 -168287.3 84209.71
## 
## Random effects:
##  Formula: ~1 | net
##         (Intercept)   Residual
## StdDev:  0.01400798 0.03051506
## 
## Variance function:
##  Structure: Exponential of variance covariate
##  Formula: ~absInStrT_sqrt 
##  Parameter estimates:
##     expon 
## 0.5003005 
## Fixed effects: s_g_area_abs ~ (absInStrT_sqrt + absOutStrT_sqrt) * topo 
##                             Value    Std.Error    DF  t-value p-value
## (Intercept)             0.8948130 0.0013090910 57540 683.5377   0e+00
## absInStrT_sqrt         -0.0394919 0.0007829890 57540 -50.4373   0e+00
## absOutStrT_sqrt         0.0292661 0.0005762394 57540  50.7881   0e+00
## topoBA                  0.0224292 0.0026763460  2997   8.3805   0e+00
## topoWS                  0.0141659 0.0019184405  2997   7.3841   0e+00
## absInStrT_sqrt:topoBA   0.0139373 0.0016258567 57540   8.5723   0e+00
## absInStrT_sqrt:topoWS  -0.0054309 0.0010813112 57540  -5.0225   0e+00
## absOutStrT_sqrt:topoBA -0.0171635 0.0006879068 57540 -24.9504   0e+00
## absOutStrT_sqrt:topoWS -0.0028399 0.0008415108 57540  -3.3748   7e-04
##  Correlation: 
##                        (Intr) abIST_ abOST_ topoBA topoWS aIST_:B aIST_:W
## absInStrT_sqrt         -0.654                                            
## absOutStrT_sqrt        -0.670  0.082                                     
## topoBA                 -0.489  0.320  0.328                              
## topoWS                 -0.682  0.446  0.457  0.334                       
## absInStrT_sqrt:topoBA   0.315 -0.482 -0.039 -0.841 -0.215                
## absInStrT_sqrt:topoWS   0.474 -0.724 -0.059 -0.232 -0.655  0.349         
## absOutStrT_sqrt:topoBA  0.561 -0.068 -0.838 -0.564 -0.383  0.211   0.050 
## absOutStrT_sqrt:topoWS  0.459 -0.056 -0.685 -0.224 -0.703  0.027   0.117 
##                        aOST_:B
## absInStrT_sqrt                
## absOutStrT_sqrt               
## topoBA                        
## topoWS                        
## absInStrT_sqrt:topoBA         
## absInStrT_sqrt:topoWS         
## absOutStrT_sqrt:topoBA        
## absOutStrT_sqrt:topoWS  0.574 
## 
## Standardized Within-Group Residuals:
##        Min         Q1        Med         Q3        Max 
## -8.8776585 -0.3479205  0.2051624  0.6193280  2.5547659 
## 
## Number of Observations: 60546
## Number of Groups: 3000
r.squaredGLMM(lmeModel)
##            R2m       R2c
## [1,] 0.4347666 0.5331459
lmeModel <- lme(s_g_area_abs ~ absInStrT_sqrt + absOutStrT_sqrt + topo, 
                data = respondedGenes,
                weights = varExp(form = ~absInStrT_sqrt),
                random = ~1|net,
                method = "ML") 
summary(lmeModel)
## Linear mixed-effects model fit by maximum likelihood
##  Data: respondedGenes 
##         AIC       BIC   logLik
##   -167224.2 -167152.1 83620.09
## 
## Random effects:
##  Formula: ~1 | net
##         (Intercept)   Residual
## StdDev:  0.01390728 0.03089286
## 
## Variance function:
##  Structure: Exponential of variance covariate
##  Formula: ~absInStrT_sqrt 
##  Parameter estimates:
##     expon 
## 0.4987068 
## Fixed effects: s_g_area_abs ~ absInStrT_sqrt + absOutStrT_sqrt + topo 
##                      Value    Std.Error    DF   t-value p-value
## (Intercept)      0.9114564 0.0008996411 57544 1013.1333       0
## absInStrT_sqrt  -0.0400760 0.0005095330 57544  -78.6524       0
## absOutStrT_sqrt  0.0178831 0.0002745940 57544   65.1256       0
## topoBA           0.0129268 0.0009730976  2997   13.2842       0
## topoWS           0.0050655 0.0007950180  2997    6.3716       0
##  Correlation: 
##                 (Intr) abIST_ abOST_ topoBA
## absInStrT_sqrt  -0.647                     
## absOutStrT_sqrt -0.531  0.176              
## topoBA          -0.194 -0.170 -0.186       
## topoWS          -0.422 -0.034 -0.030  0.429
## 
## Standardized Within-Group Residuals:
##        Min         Q1        Med         Q3        Max 
## -8.7352837 -0.3681114  0.2126254  0.6257409  2.5669098 
## 
## Number of Observations: 60546
## Number of Groups: 3000
r.squaredGLMM(lmeModel)
##           R2m       R2c
## [1,] 0.406898 0.5068415

4 Correlograms

# subset
ave_evolMetricsColnames_ofInterest <- c("ave_varP_1", "ave_relDeltaVar_10000", "ave_s_g_area_abs")

# There are also "num_generations", "num_nodes", "dens", "pop_size" columns, but they are identical for all topos.

# global net metrics
globalMetrics_forCorrs_sel <- netSelResults[, c(ave_evolMetricsColnames_ofInterest, globalNetMetricsColnames)]
globalMetrics_forCorrs_neu <- netSelResults[, c(ave_evolMetricsColnames_ofInterest, globalNetMetricsColnames)]

# gene-specific metrics
geneMetrics_forCorrs_sel <- selResults[, c(evolMetricsColnames_ofInterest, geneSpecificNetMetricsColnames_ofInterest)]
geneMetrics_forCorrs_neu <- neutrResults[, c(evolMetricsColnames_ofInterest, geneSpecificNetMetricsColnames_ofInterest)]

4.1 Gene-specific metrics

# selection
geneSpecificCorrs_sel <- rcorr(as.matrix(geneMetrics_forCorrs_sel), type = "spearman")

# neutrality
geneSpecificCorrs_neu <- rcorr(as.matrix(geneMetrics_forCorrs_neu), type = "spearman")
png(filename = paste0(pathToPlotsFolder, "/correlations_geneMetrics_sel.png"),
    width = 25, height = 25, units = 'cm', res = 300)
corrplot(geneSpecificCorrs_sel$r, type = "upper", method = "color", diag = FALSE, addCoef.col = "black",
         number.cex = 0.7,
         p.mat = geneSpecificCorrs_sel$P, sig.level = 0.05, insig = "blank",
         tl.col = "black", na.label = "NA", tl.srt = 45, col = brewer.pal(n = 8, name = "RdBu"),  outline = TRUE, mar=c(0,0,1,0))
dev.off()
## png 
##   2
tiff(filename = paste0(pathToPlotsFolder, "/correlations_geneMetrics_sel.tiff"),
    width = 25, height = 25, units = 'cm', res = 300)
corrplot(geneSpecificCorrs_sel$r, type = "upper", method = "color", diag = FALSE, addCoef.col = "black",
         number.cex = 0.7,
         p.mat = geneSpecificCorrs_sel$P, sig.level = 0.05, insig = "blank",
         tl.col = "black", na.label = "NA", tl.srt = 45, col = brewer.pal(n = 8, name = "RdBu"),  outline = TRUE, mar=c(0,0,1,0))
dev.off()
## png 
##   2
png(filename = paste0(pathToPlotsFolder, "/correlations_geneMetrics_neu.png"),
    width = 25, height = 25, units = 'cm', res = 300)
corrplot(geneSpecificCorrs_neu$r, type = "upper", method = "color", diag = FALSE, addCoef.col = "black",
         number.cex = 0.7,
         p.mat = geneSpecificCorrs_neu$P, sig.level = 0.05, insig = "blank",
         tl.col = "black", na.label = "NA", tl.srt = 45, col = brewer.pal(n = 8, name = "RdBu"),  outline = TRUE, mar=c(0,0,1,0))
dev.off()
## png 
##   2
tiff(filename = paste0(pathToPlotsFolder, "/correlations_geneMetrics_neu.tiff"),
    width = 25, height = 25, units = 'cm', res = 300)
corrplot(geneSpecificCorrs_neu$r, type = "upper", method = "color", diag = FALSE, addCoef.col = "black",
         number.cex = 0.7,
         p.mat = geneSpecificCorrs_neu$P, sig.level = 0.05, insig = "blank",
         tl.col = "black", na.label = "NA", tl.srt = 45, col = brewer.pal(n = 8, name = "RdBu"),  outline = TRUE, mar=c(0,0,1,0))
dev.off()
## png 
##   2

4.2 Global network metrics

# selection
globalCorrs_sel <- rcorr(as.matrix(globalMetrics_forCorrs_sel), type = "spearman")

# neutrality
globalCorrs_neu <- rcorr(as.matrix(globalMetrics_forCorrs_neu), type = "spearman")
png(filename = paste0(pathToPlotsFolder, "/correlations_globalMetrics_sel.png"),
    width = 20, height = 20, units = 'cm', res = 300)
corrplot(globalCorrs_sel$r, type = "upper", method = "color", diag = FALSE, addCoef.col = "black",
         number.cex = 0.8,
         p.mat = globalCorrs_sel$P, sig.level = 0.05, insig = "blank",
         tl.col = "black", na.label = "NA", tl.srt = 45, col = brewer.pal(n = 8, name = "RdBu"),  outline = TRUE, mar=c(0,0,1,0))
dev.off()
## png 
##   2
tiff(filename = paste0(pathToPlotsFolder, "/correlations_globalMetrics_sel.tiff"),
    width = 20, height = 20, units = 'cm', res = 300)
corrplot(globalCorrs_sel$r, type = "upper", method = "color", diag = FALSE, addCoef.col = "black",
         number.cex = 0.8,
         p.mat = globalCorrs_sel$P, sig.level = 0.05, insig = "blank",
         tl.col = "black", na.label = "NA", tl.srt = 45, col = brewer.pal(n = 8, name = "RdBu"),  outline = TRUE, mar=c(0,0,1,0))
dev.off()
## png 
##   2
png(filename = paste0(pathToPlotsFolder, "/correlations_globalMetrics_neu.png"),
    width = 20, height = 20, units = 'cm', res = 300)
corrplot(globalCorrs_neu$r, type = "upper", method = "color", diag = FALSE, addCoef.col = "black",
         number.cex = 0.8,
         p.mat = globalCorrs_neu$P, sig.level = 0.05, insig = "blank",
         tl.col = "black", na.label = "NA", tl.srt = 45, col = brewer.pal(n = 8, name = "RdBu"),  outline = TRUE, mar=c(0,0,1,0))
dev.off()
## png 
##   2
tiff(filename = paste0(pathToPlotsFolder, "/correlations_globalMetrics_neu.tiff"),
    width = 20, height = 20, units = 'cm', res = 300)
corrplot(globalCorrs_neu$r, type = "upper", method = "color", diag = FALSE, addCoef.col = "black",
         number.cex = 0.8,
         p.mat = globalCorrs_neu$P, sig.level = 0.05, insig = "blank",
         tl.col = "black", na.label = "NA", tl.srt = 45, col = brewer.pal(n = 8, name = "RdBu"),  outline = TRUE, mar=c(0,0,1,0))
dev.off()
## png 
##   2

5 PCA of global network metrics

globalMetrics_forPCA <- netAllResults[, globalNetMetricsColnames]
colnames(globalMetrics_forPCA) <- c("diameter", "mean path distance", "degree assortativity", "degree centralization",
                                         "indegree centralization", "outdegree centralization", "closeness centralization", 
                                         "betweenness centralization", "average degree", "average indegree", "average outdegree")

dudi <- dudi.pca(globalMetrics_forPCA, center = TRUE, scale = TRUE, nf = 10, scannf = FALSE)

plot_biplot <- fviz_pca_biplot(dudi, 
                               geom.ind = "point",
                               col.ind = netAllResults$topo,
                               col.var = "black",
                               repel = TRUE,
                               addEllipses = TRUE,
                               legend.title = "Topology") +
                               scale_colour_manual(values = topoColors)
plot_biplot

plot_scree <- fviz_eig(dudi, addlabels = TRUE)
plot_corCircle <- fviz_pca_var(dudi, col.var = "contrib", labelsize = 4, repel = TRUE) + 
                                scale_color_gradient2(low = "white", mid = "blue", high = "black") 

plot_PCA <- plot_grid(plot_scree, plot_corCircle, 
                               scale = c(0.95, 0.95),
                               labels = "AUTO",
                               label_size = 20,
                               label_fontface = "bold",
                               ncol = 2)

ggsave(filename = sprintf("plot_PCA.png"),
       plot = plot_PCA,
       path = pathToPlotsFolder, bg = 'white',
       device = "png", scale = 2, width = 18, height = 9, units = "cm",
       dpi = 300, limitsize = TRUE)
ggsave(filename = sprintf("plot_PCA.tiff"),
       plot = plot_PCA,
       path = pathToPlotsFolder, bg = 'white',
       device = "tiff", scale = 2, width = 18, height = 9, units = "cm",
       dpi = 300, limitsize = TRUE)

netAllResults$PC1<- -dudi$li$Axis1
netAllResults$PC2<- -dudi$li$Axis2

ave_responseToSel <- netSelResults$ave_responseToSel
netSelResults <- netAllResults[netAllResults$scen == "sel", ]
netSelResults$ave_responseToSel <- ave_responseToSel
netNeuResults <- netAllResults[netAllResults$scen == "neu", ]
# just selection
plot_PC1_topos <- ggplot(netSelResults, aes(y = PC1, x = topo)) +
  geom_violin(fill = noiseColor, color = "black", trim = TRUE) +
  geom_boxplot(width = 0.1, alpha = 1, outlier.alpha = 0, fill = "white") +
  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
               hjust = 1.25, vjust = -2, color = "black", aes(label = round(..y.., digits = 3))) +
  stat_compare_means(comparisons = my_comparisons, label = "p.signif") +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  scale_fill_manual(values = c("sel" = noiseColor, "neutr" = noiseColor)) +
  labs(x = "Network topology",
       y = expression(bold("PC1 (diameter + centralization)")))
plot_PC1_topos

plot_PC2_topos <- ggplot(netSelResults, aes(y = PC2, x = topo)) +
  geom_violin(fill = noiseColor, color = "black", trim = TRUE) +
  geom_boxplot(width = 0.1, alpha = 1, outlier.alpha = 0, fill = "white") +
  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
               hjust = 1.25, vjust = -2, color = "black", aes(label = round(..y.., digits = 3))) +
  stat_compare_means(comparisons = my_comparisons, label = "p.signif") +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  scale_fill_manual(values = c("sel" = noiseColor, "neutr" = noiseColor)) +
  labs(x = "Network topology",
       y = expression(bold("PC2 (average degree)")))
plot_PC2_topos

plot_netMetric <- ggplot(netSelResults, aes(y = diam, x = topo)) +
  geom_violin(fill = noiseColor, color = "black", trim = TRUE) +
  geom_boxplot(width = 0.1, alpha = 1, outlier.alpha = 0, fill = "white") +
  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
               hjust = 1.25, vjust = -2, color = "black", aes(label = round(..y.., digits = 3))) +
  stat_compare_means(comparisons = my_comparisons, label = "p.signif") +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  scale_fill_manual(values = c("sel" = noiseColor, "neutr" = noiseColor)) +
  labs(x = "Network topology",
       y = expression(bold("Diameter")))
plot_netMetric

plot_netMetric <- ggplot(netSelResults, aes(y = cntr_indegr, x = topo)) +
  geom_violin(fill = noiseColor, color = "black", trim = TRUE) +
  geom_boxplot(width = 0.1, alpha = 1, outlier.alpha = 0, fill = "white") +
  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
               hjust = 1.25, vjust = -2, color = "black", aes(label = round(..y.., digits = 3))) +
  stat_compare_means(comparisons = my_comparisons, label = "p.signif") +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  scale_fill_manual(values = c("sel" = noiseColor, "neutr" = noiseColor)) +
  labs(x = "Network topology",
       y = expression(bold("Indegree centralization")))
plot_netMetric

plot_netMetric <- ggplot(netSelResults, aes(y = cntr_outdegr, x = topo)) +
  geom_violin(fill = noiseColor, color = "black", trim = TRUE) +
  geom_boxplot(width = 0.1, alpha = 1, outlier.alpha = 0, fill = "white") +
  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
               hjust = 1.25, vjust = -2, color = "black", aes(label = round(..y.., digits = 3))) +
  stat_compare_means(comparisons = my_comparisons, label = "p.signif") +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  scale_fill_manual(values = c("sel" = noiseColor, "neutr" = noiseColor)) +
  labs(x = "Network topology",
       y = expression(bold("Outdegree centralization")))
plot_netMetric

plot_netMetric <- ggplot(netSelResults, aes(y = ave_k_all_inclps, x = topo)) +
  geom_violin(fill = noiseColor, color = "black", trim = TRUE) +
  geom_boxplot(width = 0.1, alpha = 1, outlier.alpha = 0, fill = "white") +
  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
               hjust = 1.25, vjust = -2, color = "black", aes(label = round(..y.., digits = 3))) +
  stat_compare_means(comparisons = my_comparisons, label = "p.signif") +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  scale_fill_manual(values = c("sel" = noiseColor, "neutr" = noiseColor)) +
  labs(x = "Network topology",
       y = expression(bold("Average degree")))
plot_netMetric

plot_netMetric <- ggplot(netSelResults, aes(y = ave_k_in_inclps, x = topo)) +
  geom_violin(fill = noiseColor, color = "black", trim = TRUE) +
  geom_boxplot(width = 0.1, alpha = 1, outlier.alpha = 0, fill = "white") +
  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
               hjust = 1.25, vjust = -2, color = "black", aes(label = round(..y.., digits = 3))) +
  stat_compare_means(comparisons = my_comparisons, label = "p.signif") +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  scale_fill_manual(values = c("sel" = noiseColor, "neutr" = noiseColor)) +
  labs(x = "Network topology",
       y = expression(bold("Average indegree")))
plot_netMetric

plot_netMetric <- ggplot(netSelResults, aes(y = ave_k_out_inclps, x = topo)) +
  geom_violin(fill = noiseColor, color = "black", trim = TRUE) +
  geom_boxplot(width = 0.1, alpha = 1, outlier.alpha = 0, fill = "white") +
  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
               hjust = 1.25, vjust = -2, color = "black", aes(label = round(..y.., digits = 3))) +
  stat_compare_means(comparisons = my_comparisons, label = "p.signif") +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  scale_fill_manual(values = c("sel" = noiseColor, "neutr" = noiseColor)) +
  labs(x = "Network topology",
       y = expression(bold("Average outdegree")))
plot_netMetric

6 LMs with PCs

6.1 Number of responded genes

lmModel <- lm(ave_responseToSel ~ PC1 + PC2, 
                   data = netSelResults)
summary(lmModel)
## 
## Call:
## lm(formula = ave_responseToSel ~ PC1 + PC2, data = netSelResults)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -24.0155  -1.8104   0.1247   2.0208   8.8685 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 20.18200    0.05508  366.39   <2e-16 ***
## PC1          2.56846    0.02213  116.08   <2e-16 ***
## PC2          1.83067    0.03077   59.49   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.017 on 2997 degrees of freedom
## Multiple R-squared:  0.8502, Adjusted R-squared:  0.8501 
## F-statistic:  8506 on 2 and 2997 DF,  p-value: < 2.2e-16
plot_PC1 <- ggplot(netSelResults, aes(y = ave_responseToSel, x = PC1)) +
  geom_point(aes(shape = topo, color = topo), alpha = 0.3, size = 2)+
  geom_abline(slope = lmModel$coefficients[2], 
              intercept = lmModel$coefficients[1],
              color = "black", linetype = "dashed", size = 1) +
  theme_bw() + 
  theme(plot.title = element_text(size=12, face="bold",),
        plot.subtitle = element_text(size=12, face="bold"),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "right") +
  scale_colour_manual(values = topoColors) +
  labs(x = expression(bold("PC1 (diameter + centralization)")),
       y = expression(paste(bold("Average # responded genes"))))
plot_PC1

plot_PC2 <- ggplot(netSelResults, aes(y = ave_responseToSel, x = PC2)) +
  geom_point(aes(shape = topo, color = topo), alpha = 0.3, size = 2)+
  geom_abline(slope = lmModel$coefficients[3], 
              intercept = lmModel$coefficients[1],
              color = "black", linetype = "dashed", size = 1) +
  theme_bw() + 
  theme(plot.title = element_text(size=12, face="bold",),
        plot.subtitle = element_text(size=12, face="bold"),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "right") +
  scale_colour_manual(values = topoColors) +
  labs(x = expression(bold("PC2 (average degree)")),
       y = expression(paste(bold("Average # responded genes"))))
plot_PC2

# just selection
numResponded <- table(selResults$topo, selResults$responseToSel)
numResponded
##     
##      FALSE  TRUE
##   ER  3778 22775
##   BA  1342 10310
##   WS  5939 27461
numTopos <- as.vector(table(selResults$topo))
numResponded[, 2]/numTopos
##        ER        BA        WS 
## 0.8577185 0.8848266 0.8221856
#plot_numRespondedGenes <- ggplot(respondedGenes, aes(y = , x = topo)) +
#  geom_violin(fill = genotypeColor, color = "black", trim = TRUE) +
#  geom_boxplot(width = 0.1, alpha = 1, outlier.alpha = 0, fill = "white") +
#  stat_summary(fun = mean, geom = "text", show.legend = FALSE, size = 5,
#               hjust = 1.25, vjust = 3, color = "black", aes(label = round(..y.., digits = 3))) +
#  stat_compare_means(comparisons = my_comparisons, label = "p.signif", method = "wilcox.test") +
#  theme_pubclean() + 
#  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
#        axis.title.x = element_text(size=16, face="bold"),
#        axis.title.y = element_text(size=16, face="bold"),
#        axis.text.x = element_text(size=10, face="bold"),
#        axis.text.y = element_text(size=10, face="bold")) +
#  scale_fill_manual(values = c("sel" = genotypeColor, "neutr" = genotypeColor)) +
#  labs(x = "Network topology",
#       y = expression(paste(bold("Selective pressure "), "|", bold(p), "|")))

#plot_numRespondedGenes
#ggsave(filename = sprintf("plot_numRespondedGenes.png"),
#       plot = plot_numRespondedGenes, 
#       device = "png", scale = 2, width = 6, height = 5.5, units = "cm",
#       dpi = 300, limitsize = TRUE)

6.2 Average expression variance, gen 1

numPermutations = 10000
binNum = 30

# observed MI
obs_MI_PC1 <- calcInformation(netSelResults$ave_varP_1, 
                                         netSelResults$PC1, binNum)
obs_MI_PC2 <- calcInformation(netSelResults$ave_varP_1, 
                                          netSelResults$PC2, binNum)

# create MI null distributions from permutations
MI_nullDistr_PC1 <- vector(mode = "numeric", length = numPermutations)
MI_nullDistr_PC2 <- vector(mode = "numeric", length = numPermutations)

for(permNum in 1:numPermutations)
{
  MI_nullDistr_PC1[permNum] <- 
    calcInformation(netSelResults$ave_varP_1, 
                    sample(netSelResults$PC1, 
                           size = length(netSelResults$PC1)),
                    binNum)
  MI_nullDistr_PC2[permNum] <- 
    calcInformation(netSelResults$ave_varP_1, 
                    sample(netSelResults$PC2, 
                           size = length(netSelResults$PC2)),
                    binNum)
}

# pvals for observed MI and R 
pval_MI_absInStrT <- 
  (length(which(MI_nullDistr_PC1 > obs_MI_PC1)) + 1)/numPermutations
pval_MI_absOutStrT <-
  (length(which(MI_nullDistr_PC2 > obs_MI_PC2)) + 1)/numPermutations

# pvals for observed MI and R 
pval_MI_absInStrT <- 
  (length(which(MI_nullDistr_PC1 > obs_MI_PC1)) + 1)/numPermutations
pval_MI_absOutStrT <-
  (length(which(MI_nullDistr_PC2 > obs_MI_PC2)) + 1)/numPermutations

# title
if(pval_MI_absInStrT == 1e-04) {
  MI_obs_explVar1_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC1, digits = 2), "; p $\\leq$ 10^{-4}"))
} else {
  MI_obs_explVar1_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC1, digits = 2), "; p = ",  round(pval_MI_absInStrT, digits = 2)))
}

if(pval_MI_absOutStrT == 1e-04) {
  MI_obs_explVar2_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC2, digits = 2), "; p $\\leq$ 10^{-4}"))
} else {
  MI_obs_explVar2_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC2, digits = 2), "; p = ",  round(pval_MI_absOutStrT, digits = 2)))
}

# write MI and p values to text file
sink(paste0("../results/", jointResultsFolder, "/infoMeasures_ave_varP_1-PCs.txt"))
cat(paste0("Variables: ave_varP_1; PC1\n",
    "Observed MI: ", obs_MI_PC1, "; pval: ", pval_MI_absInStrT, "\n", 
    "Variables: ave_varP_1; PC2\n",
    "Observed MI: ", obs_MI_PC2, "; pval: ", pval_MI_absOutStrT, "\n"))
## Variables: ave_varP_1; PC1
## Observed MI: 0.170000421535257; pval: 0.0133
## Variables: ave_varP_1; PC2
## Observed MI: 0.185751175769187; pval: 1e-04
sink()
lmModel <- lm(ave_varP_1 ~ PC1 + PC2, 
                data = netSelResults)
summary(lmModel)
## 
## Call:
## lm(formula = ave_varP_1 ~ PC1 + PC2, data = netSelResults)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -264.44  -78.32  -16.41   64.70  612.82 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  360.055      2.016 178.564  < 2e-16 ***
## PC1            5.827      0.810   7.194 7.92e-13 ***
## PC2           11.655      1.127  10.346  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 110.4 on 2997 degrees of freedom
## Multiple R-squared:  0.05032,    Adjusted R-squared:  0.04969 
## F-statistic:  79.4 on 2 and 2997 DF,  p-value: < 2.2e-16
r.squaredGLMM(lmModel)
##             R2m        R2c
## [1,] 0.05028804 0.05028804
# partial R^2
library(rstatix)
partial_R2_PC1 <- partial_eta_squared(lmModel)[1]
partial_R2_PC2 <- partial_eta_squared(lmModel)[2]

# R2m for plotting
partial_R2m_absInStr_num <- round(partial_R2_PC1, digits = 2)
partial_R2m_absOutStr_num <- round(partial_R2_PC2, digits = 2)
R2m_absInStr_text <- TeX(paste0("partial R^{2} = ", partial_R2m_absInStr_num))
R2m_absOutStr_text <- TeX(paste0("partial R^{2} = ", partial_R2m_absOutStr_num))

# get fitted coefficients from the model fit
coef_explVar1 <- signif(summary(lmModel)$coefficients[2, 1], digits = 2)
coef_explVar2 <- signif(summary(lmModel)$coefficients[3, 1], digits = 3)

# get p values from the model fit
pval_explVar1 <- signif(summary(lmModel)$coefficients[2, 4], digits = 2)
pval_explVar2 <- signif(summary(lmModel)$coefficients[3, 4], digits = 2)

# double check that the p values are zero before renaming them
if(summary(lmModel)$coefficients[2, 4] < 2.2e-16){pval_coef1_title = "p < 2.2 x 10^{-16}"} else
  {pval_coef1_title = paste0("p = ", pval_explVar1)}
if(summary(lmModel)$coefficients[3, 4] < 2.2e-16){pval_coef2_title = "p < 2.2 x 10^{-16}"} else 
  {pval_coef2_title = paste0("p = ", pval_explVar2)}

coef_pval_explVar1_title <- TeX(paste0("$\\beta$ = ", coef_explVar1, "; ", pval_coef1_title))
coef_pval_explVar2_title <- TeX(paste0("$\\beta$ = ", coef_explVar2, "; ", pval_coef2_title))

plot_PC1 <- ggplot(netSelResults, aes(y = ave_varP_1, x = PC1)) +
  geom_point(aes(shape = topo, color = topo), alpha = 0.3, size = 2)+
  geom_abline(slope = lmModel$coefficients[2], 
              intercept = lmModel$coefficients[1],
              color = "black", linetype = "dashed", size = 1) +
  theme_bw() + 
  theme(plot.title = element_text(size=12, face="bold",),
        plot.subtitle = element_text(size=12, face="bold"),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "right") +
  scale_colour_manual(values = topoColors) +
  labs(x = expression(bold("PC1 (diameter + centralization)")),
       y = expression(paste(bold("Expression variance, gen. 1"))),
       title = coef_pval_explVar1_title,
       subtitle = R2m_absInStr_text,
       color = "Topology",
       shape = "Topology") + 
  annotate('text', x = -3, y = 750, label = MI_obs_explVar1_title_with_pval, parse = TRUE, size = 4,  hjust = 0)
plot_PC1
## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'

plot_PC2 <- ggplot(netSelResults, aes(y = ave_varP_1, x = PC2)) +
  geom_point(aes(shape = topo, color = topo), alpha = 0.3, size = 2)+
  geom_abline(slope = lmModel$coefficients[3], 
              intercept = lmModel$coefficients[1],
              color = "black", linetype = "dashed", size = 1) +
  theme_bw() + 
  theme(plot.title = element_text(size=12, face="bold",),
        plot.subtitle = element_text(size=12, face="bold"),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "right") +
  scale_colour_manual(values = topoColors) +
  labs(x = expression(bold("PC2 (average degree)")),
       y = expression(paste(bold("Expression variance, gen. 1"))),
       title = coef_pval_explVar2_title,
       subtitle = R2m_absOutStr_text,
       color = "Topology",
       shape = "Topology") +
  annotate('text', x = -3, y = 750, label = MI_obs_explVar2_title_with_pval, parse = TRUE, size = 4,  hjust = 0)

plot_PC2
## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'

plot_netPropertiesFigure <- plot_grid(plot_PC1, plot_PC2,
                                      labels = "AUTO",
                                      label_size = 20,
                                      label_fontface = "bold")
## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'

## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'
ggsave(filename = sprintf("plot_netPropertiesFigure_averageExprVar.png"),
       plot = plot_netPropertiesFigure, 
       bg = "white",
       path = pathToPlotsFolder, 
       device = "png", 
       scale = 2, height = 800, width = 1500, units = "px",
       dpi = 300, limitsize = TRUE)
ggsave(filename = sprintf("plot_netPropertiesFigure_averageExprVar.tiff"),
       plot = plot_netPropertiesFigure, 
       bg = "white",
       path = pathToPlotsFolder, 
       device = "tiff", 
       scale = 2, height = 800, width = 1500, units = "px",
       dpi = 300, limitsize = TRUE)

6.3 Change of expression variance

numPermutations = 10000
binNum = 30

# observed MI
obs_MI_PC1 <- calcInformation(netSelResults$ave_relDeltaVar_10000, 
                                         netSelResults$PC1, binNum)
obs_MI_PC2 <- calcInformation(netSelResults$ave_relDeltaVar_10000, 
                                          netSelResults$PC2, binNum)

# create MI null distributions from permutations
MI_nullDistr_PC1 <- vector(mode = "numeric", length = numPermutations)
MI_nullDistr_PC2 <- vector(mode = "numeric", length = numPermutations)

for(permNum in 1:numPermutations)
{
  MI_nullDistr_PC1[permNum] <- 
    calcInformation(netSelResults$ave_relDeltaVar_10000, 
                    sample(netSelResults$PC1, 
                           size = length(netSelResults$PC1)),
                    binNum)
  MI_nullDistr_PC2[permNum] <- 
    calcInformation(netSelResults$ave_relDeltaVar_10000, 
                    sample(netSelResults$PC2, 
                           size = length(netSelResults$PC2)),
                    binNum)
}

# pvals for observed MI and R 
pval_MI_absInStrT <- 
  (length(which(MI_nullDistr_PC1 > obs_MI_PC1)) + 1)/numPermutations
pval_MI_absOutStrT <-
  (length(which(MI_nullDistr_PC2 > obs_MI_PC2)) + 1)/numPermutations

# pvals for observed MI and R 
pval_MI_absInStrT <- 
  (length(which(MI_nullDistr_PC1 > obs_MI_PC1)) + 1)/numPermutations
pval_MI_absOutStrT <-
  (length(which(MI_nullDistr_PC2 > obs_MI_PC2)) + 1)/numPermutations

# title
if(pval_MI_absInStrT == 1e-04) {
  MI_obs_explVar1_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC1, digits = 2), "; p $\\leq$ 10^{-4}"))
} else {
  MI_obs_explVar1_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC1, digits = 2), "; p = ",  round(pval_MI_absInStrT, digits = 2)))
}

if(pval_MI_absOutStrT == 1e-04) {
  MI_obs_explVar2_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC2, digits = 2), "; p $\\leq$ 10^{-4}"))
} else {
  MI_obs_explVar2_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC2, digits = 2), "; p = ",  round(pval_MI_absOutStrT, digits = 2)))
}

# write MI and p values to text file
sink(paste0("../results/", jointResultsFolder, "/infoMeasures_ave_relDeltaVar_10000-PCs.txt"))
cat(paste0("Variables: ave_relDeltaVar_10000; PC1\n",
    "Observed MI: ", obs_MI_PC1, "; pval: ", pval_MI_absInStrT, "\n", 
    "Variables: ave_relDeltaVar_10000; PC2\n",
    "Observed MI: ", obs_MI_PC2, "; pval: ", pval_MI_absOutStrT, "\n"))
## Variables: ave_relDeltaVar_10000; PC1
## Observed MI: 0.485011441031824; pval: 1e-04
## Variables: ave_relDeltaVar_10000; PC2
## Observed MI: 0.407655804932965; pval: 1e-04
sink()
lmModel <- lm(ave_relDeltaVar_10000 ~ PC1 + PC2, 
                data = netSelResults) 
summary(lmModel)
## 
## Call:
## lm(formula = ave_relDeltaVar_10000 ~ PC1 + PC2, data = netSelResults)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.03901 -0.01456 -0.00632  0.00263  0.63883 
## 
## Coefficients:
##               Estimate Std. Error   t value Pr(>|t|)    
## (Intercept) -0.9249655  0.0007533 -1227.954   <2e-16 ***
## PC1          0.0056199  0.0003006    18.698   <2e-16 ***
## PC2          0.0005069  0.0004233     1.198    0.231    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04065 on 2910 degrees of freedom
##   (87 observations deleted due to missingness)
## Multiple R-squared:  0.1077, Adjusted R-squared:  0.107 
## F-statistic: 175.5 on 2 and 2910 DF,  p-value: < 2.2e-16
r.squaredGLMM(lmModel)
##            R2m       R2c
## [1,] 0.1075944 0.1075944
# partial R^2
library(rstatix)
partial_R2_PC1 <- partial_eta_squared(lmModel)[1]
partial_R2_PC2 <- partial_eta_squared(lmModel)[2]

# R2m for plotting
partial_R2m_absInStr_num <- round(partial_R2_PC1, digits = 2)
partial_R2m_absOutStr_num <- round(partial_R2_PC2, digits = 2)
R2m_absInStr_text <- TeX(paste0("partial R^{2} = ", partial_R2m_absInStr_num))
R2m_absOutStr_text <- TeX(paste0("partial R^{2} = ", partial_R2m_absOutStr_num))

# get fitted coefficients from the model fit
coef_explVar1 <- signif(summary(lmModel)$coefficients[2, 1], digits = 2)
coef_explVar2 <- signif(summary(lmModel)$coefficients[3, 1], digits = 3)
#if(coef_explVar2 == -0.0096){coef_explVar2 = -0.009}

# get p values from the model fit
pval_explVar1 <- signif(summary(lmModel)$coefficients[2, 4], digits = 2)
pval_explVar2 <- signif(summary(lmModel)$coefficients[3, 4], digits = 2)

# double check that the p values are zero before renaming them
if(summary(lmModel)$coefficients[2, 4] < 2.2e-16){pval_coef1_title = "p < 2.2 x 10^{-16}"} else
  {pval_coef1_title = paste0("p = ", pval_explVar1)}
if(summary(lmModel)$coefficients[3, 4] < 2.2e-16){pval_coef2_title = "p < 2.2 x 10^{-16}"} else 
  {pval_coef2_title = paste0("p = ", pval_explVar2)}

coef_pval_explVar1_title <- TeX(paste0("$\\beta$ = ", coef_explVar1, "; ", pval_coef1_title))
coef_pval_explVar2_title <- TeX(paste0("$\\beta$ = ", coef_explVar2, "; ", pval_coef2_title))

plot_PC1 <- ggplot(netSelResults, aes(y = ave_relDeltaVar_10000, x = PC1)) +
  geom_point(aes(shape = topo, color = topo), alpha = 0.3, size = 2)+
  geom_abline(slope = lmModel$coefficients[2], 
              intercept = lmModel$coefficients[1],
              color = "black", linetype = "dashed", size = 1) +
  theme_bw() + 
  theme(plot.title = element_text(size=12, face="bold",),
        plot.subtitle = element_text(size=12, face="bold"),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "right") +
  scale_colour_manual(values = topoColors) +
  labs(x = expression(bold("PC1 (diameter + centralization)")),
       y = expression(bold("Rel."~Delta~"expr. variance")),
       title = coef_pval_explVar1_title,
       subtitle = R2m_absInStr_text,
       color = "Topology",
       shape = "Topology") +
    annotate('text', x = -4, y = -0.4, label = MI_obs_explVar1_title_with_pval, parse = TRUE, size = 4,  hjust = 0)

plot_PC1
## Warning: Removed 87 rows containing missing values (geom_point).
## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'

plot_PC2 <- ggplot(netSelResults, aes(y = ave_relDeltaVar_10000, x = PC2)) +
  geom_point(aes(shape = topo, color = topo), alpha = 0.3, size = 2)+
  geom_abline(slope = lmModel$coefficients[3], 
              intercept = lmModel$coefficients[1],
              color = "black", linetype = "dashed", size = 1) +
  theme_bw() + 
  theme(plot.title = element_text(size=12, face="bold",),
        plot.subtitle = element_text(size=12, face="bold"),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "right") +
  scale_colour_manual(values = topoColors) +
  labs(x = expression(bold("PC2 (average degree)")),
       y = expression(bold("Rel."~Delta~"expr. variance")),
       title = coef_pval_explVar2_title,
       subtitle = R2m_absOutStr_text,
       color = "Topology",
       shape = "Topology") +
  annotate('text', x = -3, y = -0.4, label = MI_obs_explVar2_title_with_pval, parse = TRUE, size = 4,  hjust = 0)

plot_PC2
## Warning: Removed 87 rows containing missing values (geom_point).

## Warning: is.na() applied to non-(list or vector) of type 'expression'

plot_netPropertiesFigure <- plot_grid(plot_PC1, plot_PC2,
                                      labels = "AUTO",
                                      label_size = 20,
                                      label_fontface = "bold")
## Warning: Removed 87 rows containing missing values (geom_point).

## Warning: is.na() applied to non-(list or vector) of type 'expression'
## Warning: Removed 87 rows containing missing values (geom_point).
## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'
ggsave(filename = sprintf("plot_netPropertiesFigure_averageRelDeltaVar.png"),
       plot = plot_netPropertiesFigure, 
       bg = "white",
       path = pathToPlotsFolder, 
       device = "png", 
       scale = 2, height = 800, width = 1500, units = "px",
       dpi = 300, limitsize = TRUE)
ggsave(filename = sprintf("plot_netPropertiesFigure_averageRelDeltaVar.tiff"),
       plot = plot_netPropertiesFigure, 
       bg = "white",
       path = pathToPlotsFolder, 
       device = "tiff", 
       scale = 2, height = 800, width = 1500, units = "px",
       dpi = 300, limitsize = TRUE)
lmeModel <- lm(ave_s_g_area_abs ~ PC1 + PC2, 
                data = netSelResults)
summary(lmeModel)
## 
## Call:
## lm(formula = ave_s_g_area_abs ~ PC1 + PC2, data = netSelResults)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.68193 -0.03798  0.01123  0.04778  0.14524 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.7738156  0.0013968  554.01   <2e-16 ***
## PC1         -0.0074498  0.0005611  -13.28   <2e-16 ***
## PC2         -0.0075850  0.0007804   -9.72   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0765 on 2997 degrees of freedom
## Multiple R-squared:  0.08286,    Adjusted R-squared:  0.08225 
## F-statistic: 135.4 on 2 and 2997 DF,  p-value: < 2.2e-16
r.squaredGLMM(lmeModel)
##             R2m        R2c
## [1,] 0.08280831 0.08280831

6.4 Selective pressure

6.4.1 Neutrality

numPermutations = 10000
binNum = 30

# observed MI
obs_MI_PC1 <- calcInformation(netNeuResults$ave_s_g_area_abs, 
                                         netNeuResults$PC1, binNum)
obs_MI_PC2 <- calcInformation(netNeuResults$ave_s_g_area_abs, 
                                          netNeuResults$PC2, binNum)

# create MI null distributions from permutations
MI_nullDistr_PC1 <- vector(mode = "numeric", length = numPermutations)
MI_nullDistr_PC2 <- vector(mode = "numeric", length = numPermutations)

for(permNum in 1:numPermutations)
{
  MI_nullDistr_PC1[permNum] <- 
    calcInformation(netNeuResults$ave_s_g_area_abs, 
                    sample(netNeuResults$PC1, 
                           size = length(netNeuResults$PC1)),
                    binNum)
  MI_nullDistr_PC2[permNum] <- 
    calcInformation(netNeuResults$ave_s_g_area_abs, 
                    sample(netNeuResults$PC2, 
                           size = length(netNeuResults$PC2)),
                    binNum)
}

# pvals for observed MI and R 
pval_MI_absInStrT <- 
  (length(which(MI_nullDistr_PC1 > obs_MI_PC1)) + 1)/numPermutations
pval_MI_absOutStrT <-
  (length(which(MI_nullDistr_PC2 > obs_MI_PC2)) + 1)/numPermutations

# pvals for observed MI and R 
pval_MI_absInStrT <- 
  (length(which(MI_nullDistr_PC1 > obs_MI_PC1)) + 1)/numPermutations
pval_MI_absOutStrT <-
  (length(which(MI_nullDistr_PC2 > obs_MI_PC2)) + 1)/numPermutations

# title
if(pval_MI_absInStrT == 1e-04) {
  MI_obs_explVar1_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC1, digits = 2), "; p $\\leq$ 10^{-4}"))
} else {
  MI_obs_explVar1_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC1, digits = 2), "; p = ",  round(pval_MI_absInStrT, digits = 2)))
}

if(pval_MI_absOutStrT == 1e-04) {
  MI_obs_explVar2_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC2, digits = 2), "; p $\\leq$ 10^{-4}"))
} else {
  MI_obs_explVar2_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC2, digits = 2), "; p = ",  round(pval_MI_absOutStrT, digits = 2)))
}

# write MI and p values to text file
sink(paste0("../results/", jointResultsFolder, "/infoMeasures_s_g_area_abs-PCs_neutrality.txt"))
cat(paste0("Variables: ave_s_g_area_abs; PC1\n",
    "Observed MI: ", obs_MI_PC1, "; pval: ", pval_MI_absInStrT, "\n", 
    "Variables: ave_s_g_area_abs; PC2\n",
    "Observed MI: ", obs_MI_PC2, "; pval: ", pval_MI_absOutStrT, "\n"))
## Variables: ave_s_g_area_abs; PC1
## Observed MI: 0.194314377140024; pval: 1e-04
## Variables: ave_s_g_area_abs; PC2
## Observed MI: 0.18528553076832; pval: 1e-04
sink()

plot_hist_MI_obs_PC1 <- ggplot(data = data.frame(MI = MI_nullDistr_PC1), aes(x = MI)) +
  geom_histogram(fill = MIColor, color = MIColor, bins = 50, alpha = 0.5) +
  geom_vline(xintercept = obs_MI_PC1, col = MIColor, lwd = 2, lty = 2) +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  labs(x = expression(paste(bold("Mutual Information (PC1)"))), y = "count",
       title = MI_obs_explVar1_title_with_pval) +
  annotate('text', x = obs_MI_PC1, y = Inf, label = "obs", parse = TRUE, size = 4, vjust = 3, hjust = 1.5)
plot_hist_MI_obs_PC1

ggsave(filename = sprintf("plot_hist_MI_obs_PC1_neu.png"),
       path = pathToPlotsFolder,
       plot = plot_hist_MI_obs_PC1, 
       device = "png", scale = 2, width = 6, height = 6, units = "cm",
       dpi = 300, limitsize = TRUE)
plot_hist_MI_obs_PC2 <- ggplot(data = data.frame(MI = MI_nullDistr_PC2), aes(x = MI)) +
  geom_histogram(fill = MIColor, color = MIColor, bins = 50, alpha = 0.5) +
  geom_vline(xintercept = obs_MI_PC2, col = MIColor, lwd = 2, lty = 2) +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  labs(x = expression(paste(bold("Mutual Information (PC2)"))), y = "count",
       title = MI_obs_explVar2_title_with_pval) +
  annotate('text', x = obs_MI_PC2, y = Inf, label = "obs", parse = TRUE, size = 4, vjust = 3, hjust = 1.5)
plot_hist_MI_obs_PC2

ggsave(filename = sprintf("plot_hist_MI_obs_PC2_neu.png"),
       path = pathToPlotsFolder,
       plot = plot_hist_MI_obs_PC2, 
       device = "png", scale = 2, width = 6, height = 6, units = "cm",
       dpi = 300, limitsize = TRUE)
indeptest <- function(model) {
  return(Box.test(resid(model)[order(fitted(model))], type = "Ljung-Box"))
}

lmModel <- lm(ave_s_g_area_abs ~ PC1 + PC2, 
                data = netNeuResults)
summary(lmModel)
## 
## Call:
## lm(formula = ave_s_g_area_abs ~ PC1 + PC2, data = netNeuResults)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0030146 -0.0005346 -0.0000209  0.0004947  0.0045215 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 7.064e-03  1.501e-05 470.708   <2e-16 ***
## PC1         1.513e-06  6.029e-06   0.251    0.802    
## PC2         5.068e-06  8.385e-06   0.604    0.546    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000822 on 2997 degrees of freedom
## Multiple R-squared:  0.0001429,  Adjusted R-squared:  -0.0005244 
## F-statistic: 0.2141 on 2 and 2997 DF,  p-value: 0.8073
r.squaredGLMM(lmModel)
##               R2m          R2c
## [1,] 0.0001427681 0.0001427681
vif(lmModel)
## PC1 PC2 
##   1   1
shapiro.test(lmModel[['residuals']])
## 
##  Shapiro-Wilk normality test
## 
## data:  lmModel[["residuals"]]
## W = 0.99032, p-value = 2.138e-13
indeptest(lmModel)
## 
##  Box-Ljung test
## 
## data:  resid(model)[order(fitted(model))]
## X-squared = 0.2261, df = 1, p-value = 0.6344
partial_eta_squared(lmModel)
##          PC1          PC2 
## 2.100026e-05 1.218682e-04
# partial R^2
partial_R2_PC1 <- partial_eta_squared(lmModel)[1]
partial_R2_PC2 <- partial_eta_squared(lmModel)[2]

# R2m for plotting
partial_R2m_absInStr_num <- signif(partial_R2_PC1, digits = 2)
partial_R2m_absOutStr_num <- signif(partial_R2_PC2, digits = 2)
if(partial_R2m_absInStr_num == 1.5e-06){partial_R2m_absInStr_num = "1.5 x 10^{-6}"}
if(partial_R2m_absOutStr_num == 9.8e-08){partial_R2m_absOutStr_num = "9.8 x 10^{-8}"}
R2m_absInStr_text <- TeX(paste0("partial R^{2} = ", partial_R2m_absInStr_num))
R2m_absOutStr_text <- TeX(paste0("partial R^{2} = ", partial_R2m_absOutStr_num))

# get fitted coefficients from the model fit
coef_explVar1 <- signif(summary(lmModel)$coefficients[2, 1], digits = 2)
coef_explVar2 <- signif(summary(lmModel)$coefficients[3, 1], digits = 2)
if(coef_explVar1 == -2.8e-07){coef_explVar1 = "-2.8 x 10^{-7}"}
if(coef_explVar2 == -1e-07){coef_explVar2 = "-1 x 10^{-7}"}

# get p values from the model fit
pval_explVar1 <- signif(summary(lmModel)$coefficients[2, 4], digits = 2)
pval_explVar2 <- signif(summary(lmModel)$coefficients[3, 4], digits = 2)

# double check that the p values are zero before renaming them
if(summary(lmModel)$coefficients[2, 4] < 2.2e-16){pval_coef1_title = "p < 2.2 x 10^{-16}"} else
  {pval_coef1_title = paste0("p = ", pval_explVar1)}
if(summary(lmModel)$coefficients[3, 4] < 2.2e-16){pval_coef2_title = "p < 2.2 x 10^{-16}"} else 
  {pval_coef2_title = paste0("p = ", pval_explVar2)}

coef_pval_explVar1_title <- TeX(paste0("$\\beta$ = ", coef_explVar1, "; ", pval_coef1_title))
coef_pval_explVar2_title <- TeX(paste0("$\\beta$ = ", coef_explVar2, "; ", pval_coef2_title))

plot_constVar_resid <- ggplot(data = data.frame("Fitted_values" = fitted(lmModel),
                               "Pearsons_residuals" = resid(lmModel, type = "pearson")),
                        aes(x = Fitted_values, y = Pearsons_residuals)) +
                        geom_point(alpha = 0.2, size = 0.5) + 
                        theme_bw() +
                        theme(plot.title = element_text(size=8, face="bold", hjust = 0.5),
                              axis.title.x = element_text(size=8, face="bold"),
                              axis.title.y = element_text(size=8, face="bold"),
                              axis.text.x = element_text(size=6, face="bold"),
                              axis.text.y = element_text(size=6, face="bold")) +
                        annotate("label", x = 0.0070775, y = 0.0015, label = "Neutrality", size = 3) +
                        labs(x = "Fitted values", y = "Pearson's residuals") 
plot_constVar_qqResid <- ggplot(data = data.frame("Pearsons_residuals" = resid(lmModel, type = "pearson")),
                                aes(sample = Pearsons_residuals)) +
                          stat_qq(alpha = 0.2, size = 0.5) + stat_qq_line() +
                        theme_bw() +
                        theme(plot.title = element_text(size=8, face="bold", hjust = 0.5),
                              axis.title.x = element_text(size=8, face="bold"),
                              axis.title.y = element_text(size=8, face="bold"),
                              axis.text.x = element_text(size=6, face="bold"),
                              axis.text.y = element_text(size=6, face="bold")) +
                        labs(x = "Theoretical quantiles", y = "Sample quantiles",
                             title = "Normal Q-Q plot, residuals")
plot_constVar_resid

plot_constVar_qqResid

plot_PC1_selpress_neu <- ggplot(netNeuResults, aes(y = ave_s_g_area_abs, x = PC1)) +
  geom_point(aes(shape = topo, color = topo), alpha = 0.3, size = 2)+
  theme_bw() + 
  theme(plot.title = element_text(size=12, face="bold",),
        plot.subtitle = element_text(size=12, face="bold"),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "bottom",
        legend.title = element_text(size=12),
        legend.text = element_text(size=12)) +
  scale_colour_manual(values = topoColors, 
                      labels = c("random (Erdős–Rényi)", 
                                 "scale-free (Barabási–Albert)", 
                                 "small-world (Watts–Strogatz)")) +
  scale_shape_manual(values = c("ER" = 19, "BA" = 17, "WS" = 15), 
                     labels = c("random (Erdős–Rényi)", 
                               "scale-free (Barabási–Albert)", 
                               "small-world (Watts–Strogatz)")) +
  labs(x = expression(bold("PC1 (diameter + centralization)")),
       y = expression(paste(bold("Average selective pressure "), "|", bold(p), "|")),
       title = coef_pval_explVar1_title,
       subtitle = R2m_absInStr_text,
       color = "Topology",
       shape = "Topology") +
  annotate('text', x = -4, y = 0.95, label = MI_obs_explVar1_title_with_pval, parse = TRUE, size = 4,  hjust = 0) +
  ylim(0, 1)
plot_PC1_selpress_neu
## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'

plot_PC2_selpress_neu <- ggplot(netNeuResults, aes(y = ave_s_g_area_abs, x = PC2)) +
  geom_point(aes(shape = topo, color = topo), alpha = 0.3, size = 2)+
  theme_bw() + 
  theme(plot.title = element_text(size=12, face="bold",),
        plot.subtitle = element_text(size=12, face="bold"),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "bottom",
        legend.title = element_text(size=12),
        legend.text = element_text(size=12)) +
  scale_colour_manual(values = topoColors, 
                      labels = c("random (Erdős–Rényi)", 
                                 "scale-free (Barabási–Albert)", 
                                 "small-world (Watts–Strogatz)")) +
  scale_shape_manual(values = c("ER" = 19, "BA" = 17, "WS" = 15), 
                     labels = c("random (Erdős–Rényi)", 
                               "scale-free (Barabási–Albert)", 
                               "small-world (Watts–Strogatz)")) +
  labs(x = expression(bold("PC2 (average degree)")),
       y = expression(paste(bold("Average selective pressure "), "|", bold(p), "|")),
       title = coef_pval_explVar2_title,
       subtitle = R2m_absOutStr_text,
       color = "Topology",
       shape = "Topology") +
  annotate('text', x = -3, y = 0.95, label = MI_obs_explVar2_title_with_pval, parse = TRUE, size = 4,  hjust = 0) +
  scale_x_continuous(n.breaks = 4) +
  ylim(0, 1)
plot_PC2_selpress_neu
## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'

6.4.2 Selection

numPermutations = 10000
binNum = 30

# observed MI
obs_MI_PC1 <- calcInformation(netSelResults$ave_s_g_area_abs, 
                                         netSelResults$PC1, binNum)
obs_MI_PC2 <- calcInformation(netSelResults$ave_s_g_area_abs, 
                                          netSelResults$PC2, binNum)

# create MI null distributions from permutations
MI_nullDistr_PC1 <- vector(mode = "numeric", length = numPermutations)
MI_nullDistr_PC2 <- vector(mode = "numeric", length = numPermutations)

for(permNum in 1:numPermutations)
{
  MI_nullDistr_PC1[permNum] <- 
    calcInformation(netSelResults$ave_s_g_area_abs, 
                    sample(netSelResults$PC1, 
                           size = length(netSelResults$PC1)),
                    binNum)
  MI_nullDistr_PC2[permNum] <- 
    calcInformation(netSelResults$ave_s_g_area_abs, 
                    sample(netSelResults$PC2, 
                           size = length(netSelResults$PC2)),
                    binNum)
}

# pvals for observed MI and R 
pval_MI_absInStrT <- 
  (length(which(MI_nullDistr_PC1 > obs_MI_PC1)) + 1)/numPermutations
pval_MI_absOutStrT <-
  (length(which(MI_nullDistr_PC2 > obs_MI_PC2)) + 1)/numPermutations

# pvals for observed MI and R 
pval_MI_absInStrT <- 
  (length(which(MI_nullDistr_PC1 > obs_MI_PC1)) + 1)/numPermutations
pval_MI_absOutStrT <-
  (length(which(MI_nullDistr_PC2 > obs_MI_PC2)) + 1)/numPermutations

# title
if(pval_MI_absInStrT == 1e-04) {
  MI_obs_explVar1_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC1, digits = 2), "; p $\\leq$ 10^{-4}"))
} else {
  MI_obs_explVar1_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC1, digits = 2), "; p = ",  round(pval_MI_absInStrT, digits = 2)))
}

if(pval_MI_absOutStrT == 1e-04) {
  MI_obs_explVar2_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC2, digits = 2), "; p $\\leq$ 10^{-4}"))
} else {
  MI_obs_explVar2_title_with_pval <- 
  TeX(paste0("$\\MI$ = ", round(obs_MI_PC2, digits = 2), "; p = ",  round(pval_MI_absOutStrT, digits = 2)))
}

# write MI and p values to text file
sink(paste0("../results/", jointResultsFolder, "/infoMeasures_s_g_area_abs-PCs.txt"))
cat(paste0("Variables: ave_s_g_area_abs; PC1\n",
    "Observed MI: ", obs_MI_PC1, "; pval: ", pval_MI_absInStrT, "\n", 
    "Variables: ave_s_g_area_abs; PC2\n",
    "Observed MI: ", obs_MI_PC2, "; pval: ", pval_MI_absOutStrT, "\n"))
## Variables: ave_s_g_area_abs; PC1
## Observed MI: 0.266973303808035; pval: 1e-04
## Variables: ave_s_g_area_abs; PC2
## Observed MI: 0.25590923039374; pval: 1e-04
sink()

plot_hist_MI_obs_PC1 <- ggplot(data = data.frame(MI = MI_nullDistr_PC1), aes(x = MI)) +
  geom_histogram(fill = MIColor, color = MIColor, bins = 50, alpha = 0.5) +
  geom_vline(xintercept = obs_MI_PC1, col = MIColor, lwd = 2, lty = 2) +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  labs(x = expression(paste(bold("Mutual Information (PC1)"))), y = "count",
       title = MI_obs_explVar1_title_with_pval) +
  annotate('text', x = obs_MI_PC1, y = Inf, label = "obs", parse = TRUE, size = 4, vjust = 3, hjust = 1.5)
plot_hist_MI_obs_PC1

ggsave(filename = sprintf("plot_hist_MI_obs_PC1_sel.png"),
       path = pathToPlotsFolder,
       plot = plot_hist_MI_obs_PC1, 
       device = "png", scale = 2, width = 6, height = 6, units = "cm",
       dpi = 300, limitsize = TRUE)
plot_hist_MI_obs_PC2 <- ggplot(data = data.frame(MI = MI_nullDistr_PC2), aes(x = MI)) +
  geom_histogram(fill = MIColor, color = MIColor, bins = 50, alpha = 0.5) +
  geom_vline(xintercept = obs_MI_PC2, col = MIColor, lwd = 2, lty = 2) +
  theme_pubclean() + 
  theme(plot.title = element_text(size=16, face="bold", hjust = 0.5),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold")) +
  labs(x = expression(paste(bold("Mutual Information (PC2)"))), y = "count",
       title = MI_obs_explVar2_title_with_pval) +
  annotate('text', x = obs_MI_PC2, y = Inf, label = "obs", parse = TRUE, size = 4, vjust = 3, hjust = 1.5)
plot_hist_MI_obs_PC2

ggsave(filename = sprintf("plot_hist_MI_obs_PC2_sel.png"),
       path = pathToPlotsFolder,
       plot = plot_hist_MI_obs_PC2, 
       device = "png", scale = 2, width = 6, height = 6, units = "cm",
       dpi = 300, limitsize = TRUE)
indeptest <- function(model) {
  return(Box.test(resid(model)[order(fitted(model))], type = "Ljung-Box"))
}

lmModel <- lm(ave_s_g_area_abs ~ PC1 + PC2, 
                data = netSelResults)
summary(lmModel)
## 
## Call:
## lm(formula = ave_s_g_area_abs ~ PC1 + PC2, data = netSelResults)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.68193 -0.03798  0.01123  0.04778  0.14524 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.7738156  0.0013968  554.01   <2e-16 ***
## PC1         -0.0074498  0.0005611  -13.28   <2e-16 ***
## PC2         -0.0075850  0.0007804   -9.72   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0765 on 2997 degrees of freedom
## Multiple R-squared:  0.08286,    Adjusted R-squared:  0.08225 
## F-statistic: 135.4 on 2 and 2997 DF,  p-value: < 2.2e-16
r.squaredGLMM(lmModel)
##             R2m        R2c
## [1,] 0.08280831 0.08280831
vif(lmModel)
## PC1 PC2 
##   1   1
shapiro.test(lmModel[['residuals']])
## 
##  Shapiro-Wilk normality test
## 
## data:  lmModel[["residuals"]]
## W = 0.89765, p-value < 2.2e-16
indeptest(lmModel)
## 
##  Box-Ljung test
## 
## data:  resid(model)[order(fitted(model))]
## X-squared = 0.15435, df = 1, p-value = 0.6944
partial_eta_squared(lmModel)
##        PC1        PC2 
## 0.05555326 0.03056054
# partial R^2
partial_R2_PC1 <- partial_eta_squared(lmModel)[1]
partial_R2_PC2 <- partial_eta_squared(lmModel)[2]

# R2m for plotting
partial_R2m_absInStr_num <- round(partial_R2_PC1, digits = 2)
partial_R2m_absOutStr_num <- round(partial_R2_PC2, digits = 2)
R2m_absInStr_text <- TeX(paste0("partial R^{2} = ", partial_R2m_absInStr_num))
R2m_absOutStr_text <- TeX(paste0("partial R^{2} = ", partial_R2m_absOutStr_num))

# get fitted coefficients from the model fit
coef_explVar1 <- signif(summary(lmModel)$coefficients[2, 1], digits = 1)
coef_explVar2 <- signif(summary(lmModel)$coefficients[3, 1], digits = 2)
if(coef_explVar2 == -0.0096){coef_explVar2 = -0.009}

# get p values from the model fit
pval_explVar1 <- signif(summary(lmModel)$coefficients[2, 4], digits = 2)
pval_explVar2 <- signif(summary(lmModel)$coefficients[3, 4], digits = 2)

# double check that the p values are zero before renaming them
if(summary(lmModel)$coefficients[2, 4] < 2.2e-16){pval_coef1_title = "p < 2.2 x 10^{-16}"} else
  {pval_coef1_title = paste0("p = ", pval_explVar1)}
if(summary(lmModel)$coefficients[3, 4] < 2.2e-16){pval_coef2_title = "p < 2.2 x 10^{-16}"} else 
  {pval_coef2_title = paste0("p = ", pval_explVar2)}

if(pval_explVar1 == 4.9e-11) {pval_coef1_title = paste0("p = 4.9 x 10^{-11}")}

coef_pval_explVar1_title <- TeX(paste0("$\\beta$ = ", coef_explVar1, "; ", pval_coef1_title))
coef_pval_explVar2_title <- TeX(paste0("$\\beta$ = ", coef_explVar2, "; ", pval_coef2_title))

plot_constVar_resid_sel <- ggplot(data = data.frame("Fitted_values" = fitted(lmModel),
                               "Pearsons_residuals" = resid(lmModel, type = "pearson")),
                        aes(x = Fitted_values, y = Pearsons_residuals)) +
                        geom_point(alpha = 0.2, size = 0.5) + 
                        theme_bw() +
                        theme(plot.title = element_text(size=8, face="bold", hjust = 0.5),
                              axis.title.x = element_text(size=8, face="bold"),
                              axis.title.y = element_text(size=8, face="bold"),
                              axis.text.x = element_text(size=6, face="bold"),
                              axis.text.y = element_text(size=6, face="bold")) +
                        annotate("label", x = 0.75, y = -0.5, label = "Selection", size = 3) +
                        labs(x = "Fitted values", y = "Pearson's residuals") 
plot_constVar_qqResid_sel <- ggplot(data = data.frame("Pearsons_residuals" = resid(lmModel, type = "pearson")),
                                aes(sample = Pearsons_residuals)) +
                          stat_qq(alpha = 0.2, size = 0.5) + stat_qq_line() +
                        theme_bw() +
                        theme(plot.title = element_text(size=8, face="bold", hjust = 0.5),
                              axis.title.x = element_text(size=8, face="bold"),
                              axis.title.y = element_text(size=8, face="bold"),
                              axis.text.x = element_text(size=6, face="bold"),
                              axis.text.y = element_text(size=6, face="bold")) +
                        labs(x = "Theoretical quantiles", y = "Sample quantiles",
                             title = "Normal Q-Q plot, residuals")
plot_constVar_resid_sel

plot_constVar_qqResid_sel

plot_ModelDiagnostics <- plot_grid(plot_constVar_resid_sel, plot_constVar_qqResid_sel,
                                   plot_constVar_resid, plot_constVar_qqResid,
                                   ncol = 2,
                                   labels = "AUTO")
# save to plots folder
ggsave(filename = sprintf("plot_ModelDiagnostics_networkProperties.png"),
       path = pathToPlotsFolder,
       plot = plot_ModelDiagnostics, 
       device = "png", scale = 1.2, width = 12, height = 12, units = "cm",
       dpi = 300, limitsize = TRUE,
       bg = "white")
plot_PC1_selpress_sel <- ggplot(netSelResults, aes(y = ave_s_g_area_abs, x = PC1)) +
  geom_point(aes(shape = topo, color = topo), alpha = 0.3, size = 2) +
  geom_quantile(quantiles = c(.5), color = "black", size = 0.75) +
  geom_quantile(quantiles = c(.25, .75), color = "black", size = 0.5, linetype = 2) +
  theme_bw() + 
  theme(plot.title = element_text(size=12, face="bold",),
        plot.subtitle = element_text(size=12, face="bold"),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "bottom",
        legend.title = element_text(size=12),
        legend.text = element_text(size=12)) +
  scale_colour_manual(values = topoColors, 
                      labels = c("random (Erdős–Rényi)", 
                                 "scale-free (Barabási–Albert)", 
                                 "small-world (Watts–Strogatz)")) +
  scale_shape_manual(values = c("ER" = 19, "BA" = 17, "WS" = 15), 
                     labels = c("random (Erdős–Rényi)", 
                               "scale-free (Barabási–Albert)", 
                               "small-world (Watts–Strogatz)")) +
  labs(x = expression(bold("PC1 (diameter + centralization)")),
       y = expression(paste(bold("Average selective pressure "), "|", bold(p), "|")),
       title = coef_pval_explVar1_title,
       subtitle = R2m_absInStr_text,
       color = "Topology",
       shape = "Topology") +
  annotate('text', x = -4, y = 0.95, label = MI_obs_explVar1_title_with_pval, parse = TRUE, size = 4,  hjust = 0) +
  ylim(0, 1)
plot_PC1_selpress_sel
## Smoothing formula not specified. Using: y ~ x
## Smoothing formula not specified. Using: y ~ x
## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'

plot_PC2_selpress_sel <- ggplot(netSelResults, aes(y = ave_s_g_area_abs, x = PC2)) +
  geom_point(aes(shape = topo, color = topo), alpha = 0.3, size = 2) +
  geom_quantile(quantiles = c(.5), color = "black", size = 0.75) +
  geom_quantile(quantiles = c(.25, .75), color = "black", size = 0.5, linetype = 2) +
  theme_bw() + 
  theme(plot.title = element_text(size=12, face="bold",),
        plot.subtitle = element_text(size=12, face="bold"),
        axis.title.x = element_text(size=16, face="bold"),
        axis.title.y = element_text(size=16, face="bold"),
        axis.text.x = element_text(size=10, face="bold"),
        axis.text.y = element_text(size=10, face="bold"),
        legend.position = "bottom",
        legend.title = element_text(size=12),
        legend.text = element_text(size=12)) +
  scale_colour_manual(values = topoColors, 
                      labels = c("random (Erdős–Rényi)", 
                                 "scale-free (Barabási–Albert)", 
                                 "small-world (Watts–Strogatz)")) +
  scale_shape_manual(values = c("ER" = 19, "BA" = 17, "WS" = 15), 
                     labels = c("random (Erdős–Rényi)", 
                               "scale-free (Barabási–Albert)", 
                               "small-world (Watts–Strogatz)")) +
  labs(x = expression(bold("PC2 (average degree)")),
       y = expression(paste(bold("Average selective pressure "), "|", bold(p), "|")),
       title = coef_pval_explVar2_title,
       subtitle = R2m_absOutStr_text,
       color = "Topology",
       shape = "Topology") +
  annotate('text', x = -3, y = 0.95, label = MI_obs_explVar2_title_with_pval, parse = TRUE, size = 4,  hjust = 0) +
  scale_x_continuous(n.breaks = 4) +
  ylim(0, 1)
plot_PC2_selpress_sel
## Smoothing formula not specified. Using: y ~ x
## Smoothing formula not specified. Using: y ~ x
## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'

7 Final plot

jointTitle_sel <- ggdraw() + draw_label("Selection",
                                        size = 20,
                                        fontface = 'bold')
jointTitle_neu <- ggdraw() + draw_label("Neutrality", 
                                        size = 20,
                                        fontface = 'bold')
jointTitle_combined <- cowplot::plot_grid(NULL, jointTitle_sel, NULL,
                                 NULL, jointTitle_neu, NULL,
                                 labels = c("", "", "", "", "", ""),
                                 ncol = 6,
                                 rel_widths = c(0.5, 1, 0.5, 0.5, 1, 0.5))

plot_netPropertiesFigure_body <- ggpubr::ggarrange(plot_PC1_selpress_sel, plot_PC2_selpress_sel,
                                           plot_PC1_selpress_neu, plot_PC2_selpress_neu,
                                           labels = "AUTO", font.label = list(size = 20, face = "bold"),
                                           ncol = 4, nrow = 1, 
                                           common.legend = TRUE, legend = "bottom")
## Smoothing formula not specified. Using: y ~ x
## Smoothing formula not specified. Using: y ~ x
## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'
## Smoothing formula not specified. Using: y ~ x
## Smoothing formula not specified. Using: y ~ x
## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'
## Smoothing formula not specified. Using: y ~ x
## Smoothing formula not specified. Using: y ~ x
## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'

## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'

## Warning in is.na(x): is.na() applied to non-(list or vector) of type
## 'expression'
plot_netPropertiesFigure <- cowplot::plot_grid(jointTitle_combined,
                                       plot_netPropertiesFigure_body,
                                       ncol = 1,
                                       rel_heights = c(0.1, 1))

ggsave(filename = sprintf("plot_netPropertiesFigure.png"),
       plot = plot_netPropertiesFigure, 
       bg = "white",
       path = pathToPlotsFolder, 
       device = "png", 
       scale = 2.1, height = 800, width = 2250, units = "px",
       dpi = 300, limitsize = TRUE)
ggsave(filename = sprintf("plot_netPropertiesFigure.tiff"),
       plot = plot_netPropertiesFigure, 
       bg = "white",
       path = pathToPlotsFolder, 
       device = "tiff", 
       scale = 2.1, height = 900, width = 2250, units = "px",
       dpi = 300, limitsize = TRUE)
sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.5 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/atlas/libblas.so.3.10.3
## LAPACK: /usr/lib/x86_64-linux-gnu/atlas/liblapack.so.3.10.3
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB.UTF-8        LC_COLLATE=en_US.UTF-8    
##  [5] LC_MONETARY=en_GB.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_GB.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] dplyr_1.0.7        rstatix_0.7.0      FSA_0.9.3          factoextra_1.0.7  
##  [5] ade4_1.7-15        corrplot_0.90      Hmisc_4.3-1        Formula_1.2-3     
##  [9] survival_3.2-7     lattice_0.20-38    reshape2_1.4.3     latex2exp_0.4.0   
## [13] RColorBrewer_1.1-2 car_3.0-11         carData_3.0-4      lme4_1.1-27.1     
## [17] Matrix_1.2-18      infotheo_1.2.0     cowplot_1.1.1      gridExtra_2.3     
## [21] ggridges_0.5.2     ggpubr_0.4.0       ggplot2_3.3.5      MuMIn_1.43.17     
## [25] nlme_3.1-144       rmarkdown_2.10    
## 
## loaded via a namespace (and not attached):
##  [1] matrixStats_0.60.0  tools_3.6.3         backports_1.2.1    
##  [4] bslib_0.2.5.1       utf8_1.2.2          R6_2.5.1           
##  [7] rpart_4.1-15        DBI_1.1.0           colorspace_2.0-2   
## [10] nnet_7.3-12         withr_2.4.2         tidyselect_1.1.1   
## [13] curl_4.3.2          compiler_3.6.3      quantreg_5.86      
## [16] htmlTable_1.13.3    SparseM_1.81        labeling_0.4.2     
## [19] sass_0.4.0          scales_1.1.1        checkmate_2.0.0    
## [22] stringr_1.4.0       digest_0.6.28       foreign_0.8-75     
## [25] minqa_1.2.4         rio_0.5.27          base64enc_0.1-3    
## [28] jpeg_0.1-8.1        pkgconfig_2.0.3     htmltools_0.5.2    
## [31] dunn.test_1.3.5     highr_0.9           fastmap_1.1.0      
## [34] htmlwidgets_1.5.3   rlang_0.4.12        readxl_1.3.1       
## [37] rstudioapi_0.13     farver_2.1.0        jquerylib_0.1.4    
## [40] generics_0.1.0      jsonlite_1.7.2      acepack_1.4.1      
## [43] zip_2.2.0           magrittr_2.0.1      Rcpp_1.0.7         
## [46] munsell_0.5.0       fansi_0.5.0         abind_1.4-5        
## [49] lifecycle_1.0.1     stringi_1.7.3       yaml_2.2.1         
## [52] MASS_7.3-57         plyr_1.8.6          grid_3.6.3         
## [55] ggrepel_0.9.1       forcats_0.5.1       crayon_1.4.2       
## [58] haven_2.4.3         splines_3.6.3       hms_1.1.0          
## [61] knitr_1.33          pillar_1.6.4        boot_1.3-25        
## [64] ggsignif_0.6.2      stats4_3.6.3        glue_1.5.0         
## [67] evaluate_0.14       latticeExtra_0.6-29 data.table_1.14.0  
## [70] vctrs_0.3.8         png_0.1-7           nloptr_1.2.2.2     
## [73] MatrixModels_0.5-0  cellranger_1.1.0    gtable_0.3.0       
## [76] purrr_0.3.4         tidyr_1.1.3         xfun_0.25          
## [79] openxlsx_4.2.4      broom_0.7.9         conquer_1.0.2      
## [82] tibble_3.1.6        cluster_2.1.0       ellipsis_0.3.2
packageVersion('igraph')
## [1] '1.2.4.2'
packageVersion('intergraph')
## [1] '2.0.2'
packageVersion('lme4')
## [1] '1.1.27.1'
packageVersion('nlme')
## [1] '3.1.144'
packageVersion('MuMIn')
## [1] '1.43.17'
packageVersion('infotheo')
## [1] '1.2.0'
packageVersion('car')
## [1] '3.0.11'
packageVersion('ade4')
## [1] '1.7.15'